Water-Resources-Engineering-Chin.pdf

Water-Resources Engineering, Second Edition
David A. Chin

Contents
1 Introduction 1
1.1 Water-Resources Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Hydrologic Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Design of Water-Resource Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Water-Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Water-Use Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 About This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Flow in Closed Conduits 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Single Pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.3 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Pipe Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.1 Nodal Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.2 Loop Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4 Pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4.1 Aﬃnity Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4.2 Pump Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.4.3 Limits on Pump Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.4.4 Multiple-Pump Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.5 Design of Water Distribution Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.5.1 Water Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.5.2 Pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.5.3 Pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.5.4 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.5.5 Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.5.6 Fire Hydrants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.5.7 Water Storage Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.5.8 Performance Criteria for Water-Distribution Systems . . . . . . . . . . . . . . 80
2.5.9 Water Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.5.10 Network Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
iii

iv
2.6 Computer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3 Flow in Open Channels 93
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.2 Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.2.1 Steady-State Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . 94
3.2.2 Steady-State Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . 94
3.2.2.1 Darcy-Weisbach Equation . . . . . . . . . . . . . . . . . . . . . . . . 97
3.2.2.2 Manning Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.2.2.3 Velocity Distribution in Open Channels . . . . . . . . . . . . . . . . 108
3.2.3 Steady-State Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.2.3.1 Energy Grade Line . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.2.3.2 Specific Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.3 Water Surface Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.3.1 Profile Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.3.2 Classification of Water-Surface Profiles . . . . . . . . . . . . . . . . . . . . . . 122
3.3.3 Hydraulic Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.3.4 Computation of Water-Surface Profiles . . . . . . . . . . . . . . . . . . . . . . 129
3.3.4.1 Direct-Integration Method . . . . . . . . . . . . . . . . . . . . . . . 131
3.3.4.2 Direct-Step Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
3.3.4.3 Standard-Step Method . . . . . . . . . . . . . . . . . . . . . . . . . 134
3.4 Hydraulic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.4.1 Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.4.1.1 Sharp-Crested Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.4.1.2 Broad-Crested Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
3.4.2 Spillways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3.4.3 Parshall Flumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
3.4.4 Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
3.4.5 Stilling Basins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
3.4.6 Culverts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
3.5 Design of Open Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
3.5.1 Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
3.5.2 Unlined Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
3.5.3 Lined Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
3.5.3.1 Rigid-Boundary Channels . . . . . . . . . . . . . . . . . . . . . . . . 200
3.5.3.2 Flexible-Boundary Channels . . . . . . . . . . . . . . . . . . . . . . 203
3.5.4 Levees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
3.6 Design of Sanitary Sewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
3.6.1 Design Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
3.6.1.1 Service Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
3.6.1.2 Inflow and Infiltration (I/I) . . . . . . . . . . . . . . . . . . . . . . . 215
3.6.1.3 Combined Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
3.6.2 Hydraulics of Sewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
3.6.3 Sewer-Pipe Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

DRAFT as of August 25, 2004 v
3.6.4 System Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
3.6.5 Sulﬁde Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
3.6.6 Design Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
3.6.7 Force Mains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
3.7 Computer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
4 Probability and Statistics in Water-Resources Engineering 253
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
4.2 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
4.2.1 Discrete Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . 254
4.2.2 Continuous Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . 255
4.2.3 Mathematical Expectation and Moments . . . . . . . . . . . . . . . . . . . . 256
4.2.4 Return Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
4.2.5 Common Probability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 261
4.3 Analysis of Hydrologic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
4.3.1 Estimation of Population Distribution . . . . . . . . . . . . . . . . . . . . . . 281
4.3.1.1 Probability Distribution of Observed Data . . . . . . . . . . . . . . 282
4.3.1.2 Hypothesis Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
4.3.2 Estimation of Population Parameters . . . . . . . . . . . . . . . . . . . . . . . 287
4.3.2.1 Method of Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
4.3.2.2 Maximum-Likelihood Method . . . . . . . . . . . . . . . . . . . . . 290
4.3.2.3 Method of L-Moments . . . . . . . . . . . . . . . . . . . . . . . . . . 292
4.3.3 Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
5 Surface-Water Hydrology 311
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
5.2 Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
5.2.1 Local Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
5.2.2 Spatially-Averaged Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
5.2.3 Design Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
5.2.3.1 Return Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
5.2.3.2 Rainfall Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
5.2.3.3 Rainfall Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
5.2.3.4 Temporal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 329
5.2.3.5 Spatial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
5.2.3.6 Probable Maximum Precipitation, PMP . . . . . . . . . . . . . . . . 336
5.2.3.7 Probable Maximum Storm, PMS . . . . . . . . . . . . . . . . . . . . 341
5.2.3.8 Standard Project Storm . . . . . . . . . . . . . . . . . . . . . . . . . 348
5.3 Rainfall Abstractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
5.3.1 Interception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
5.3.2 Depression Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
5.3.3 Inﬁltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

vi
5.3.3.1 The Infiltration Process . . . . . . . . . . . . . . . . . . . . . . . . . 355
5.3.3.2 Horton Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
5.3.3.3 Green-Ampt Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
5.3.3.4 NRCS Curve-Number Model . . . . . . . . . . . . . . . . . . . . . . 368
5.3.3.5 Comparison of Infiltration Models . . . . . . . . . . . . . . . . . . . 373
5.3.4 Rainfall Excess on Composite Areas . . . . . . . . . . . . . . . . . . . . . . . 374
5.4 Runoff Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
5.4.1 Time of Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
5.4.1.1 Overland Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
5.4.1.2 Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
5.4.1.3 Accuracy of Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . 388
5.4.2 Peak-Runoff Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
5.4.2.1 The Rational Method . . . . . . . . . . . . . . . . . . . . . . . . . . 389
5.4.2.2 NRCS-TR55 Method . . . . . . . . . . . . . . . . . . . . . . . . . . 394
5.4.2.3 USGS Regional Regression Equations . . . . . . . . . . . . . . . . . 396
5.4.3 Continuous-Runoff Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
5.4.3.1 Unit-Hydrograph Theory . . . . . . . . . . . . . . . . . . . . . . . . 399
5.4.3.2 Unit-Hydrograph Models . . . . . . . . . . . . . . . . . . . . . . . . 407
5.4.3.3 Time-Area Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
5.4.3.4 Kinematic-Wave Model . . . . . . . . . . . . . . . . . . . . . . . . . 420
5.4.3.5 Nonlinear Reservoir Model . . . . . . . . . . . . . . . . . . . . . . . 421
5.4.3.6 Santa Barbara Urban Hydrograph Model . . . . . . . . . . . . . . . 423
5.5 Routing Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
5.5.1 Hydrologic Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
5.5.1.1 Modified Puls Method . . . . . . . . . . . . . . . . . . . . . . . . . . 426
5.5.1.2 Muskingum Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
5.5.2 Hydraulic Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
5.6 Water-Quality Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
5.6.1 USGS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
5.6.2 EPA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
5.7 Design of Stormwater Management Systems . . . . . . . . . . . . . . . . . . . . . . . 443
5.7.1 Minor System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
5.7.1.1 Storm Sewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
5.7.1.2 Street Gutters and Inlets . . . . . . . . . . . . . . . . . . . . . . . . 451
5.7.1.3 Roadside and Median Channels . . . . . . . . . . . . . . . . . . . . 470
5.7.2 Runoff Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
5.7.2.1 Stormwater Impoundments . . . . . . . . . . . . . . . . . . . . . . . 472
5.7.2.2 Flood Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
5.7.2.3 Water-Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . 480
5.7.3 Major System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
5.8 Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
5.8.1 ASCE Penman-Monteith Method . . . . . . . . . . . . . . . . . . . . . . . . . 503
5.8.2 Potential Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
5.8.3 Reference Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
5.8.3.1 FAO56-Penman-Monteith Method . . . . . . . . . . . . . . . . . . . 518

DRAFT as of August 25, 2004 vii
5.8.3.2 ASCE Standardized Method . . . . . . . . . . . . . . . . . . . . . . 523
5.8.3.3 Evaporation Pans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524
5.8.3.4 Empirical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
5.8.4 Actual Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
5.8.4.1 Crop-Coefficient Approach . . . . . . . . . . . . . . . . . . . . . . . 528
5.8.5 Selection of ET Estimation Method . . . . . . . . . . . . . . . . . . . . . . . 537
5.9 Drought . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
5.10 Computer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
5.10.1 Extreme Rainfall Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
5.10.1.1 Probable Maximum Flood . . . . . . . . . . . . . . . . . . . . . . . 566
5.10.1.2 Standard Project Flood . . . . . . . . . . . . . . . . . . . . . . . . . 567
6 Ground-Water Hydrology 569
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
6.2 Basic Equations of Ground-Water Flow . . . . . . . . . . . . . . . . . . . . . . . . . 575
6.2.1 Darcy’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575
6.2.2 General Flow Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588
6.2.3 Two-Dimensional Approximations . . . . . . . . . . . . . . . . . . . . . . . . 593
6.2.3.1 Unconfined Aquifers . . . . . . . . . . . . . . . . . . . . . . . . . . . 593
6.2.3.2 Confined Aquifers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
6.3 Solutions of the Ground-Water Flow Equation . . . . . . . . . . . . . . . . . . . . . 604
6.3.1 Steady Uniform Flow in a Confined Aquifer . . . . . . . . . . . . . . . . . . . 604
6.3.2 Steady Uniform Flow in an Unconfined Aquifer . . . . . . . . . . . . . . . . . 605
6.3.3 Steady Unconfined Flow Between Two Reservoirs . . . . . . . . . . . . . . . . 606
6.3.4 Steady Flow to a Well in a Confined Aquifer . . . . . . . . . . . . . . . . . . 609
6.3.5 Steady Flow to a Well in an Unconfined Aquifer . . . . . . . . . . . . . . . . 612
6.3.6 Steady Flow to a Well in a Leaky Confined Aquifer . . . . . . . . . . . . . . . 615
6.3.7 Steady Flow to a Well in an Unconfined Aquifer with Recharge . . . . . . . . 619
6.3.8 Unsteady Flow to a Well in a Confined Aquifer . . . . . . . . . . . . . . . . . 621
6.3.9 Unsteady Flow to a Well in an Unconfined Aquifer . . . . . . . . . . . . . . . 628
6.3.10 Unsteady Flow to a Well in a Leaky Confined Aquifer . . . . . . . . . . . . . 633
6.3.11 Partially Penetrating Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
6.4 Principle of Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642
6.4.1 Multiple Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642
6.4.2 Well in Uniform Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645
6.5 Method of Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647
6.5.1 Constant-Head Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647
6.5.2 Impermeable Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
6.5.3 Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652
6.6 Saltwater Intrusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
6.7 Ground-Water Flow in the Unsaturated Zone . . . . . . . . . . . . . . . . . . . . . . 658
6.8 Engineered Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663
6.8.1 Design of Wellfields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663
6.8.2 Design of Water-Supply Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . 666

viii
6.8.3 Performance Assessment of Water-Supply Wells . . . . . . . . . . . . . . . . . 675
6.8.4 Well Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680
6.8.5 Wellhead Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
6.8.6 Design of Aquifer Pumping Tests . . . . . . . . . . . . . . . . . . . . . . . . . 684
6.8.6.1 Design of Pumping Well . . . . . . . . . . . . . . . . . . . . . . . . . 685
6.8.6.2 Design of Observation Wells . . . . . . . . . . . . . . . . . . . . . . 686
6.8.6.3 Field Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687
6.8.7 Slug Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689
6.8.8 Design of Exﬁltration Trenches . . . . . . . . . . . . . . . . . . . . . . . . . . 695
6.8.9 Seepage Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
6.9 Computer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702
7 Water-Resources Planning and Management 715
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715
7.2 Planning Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716
7.3 Legal and Regulatory Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720
7.3.1 Water Rights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720
7.3.1.1 Surface-Water Rights . . . . . . . . . . . . . . . . . . . . . . . . . . 721
7.3.1.2 Ground-Water Rights . . . . . . . . . . . . . . . . . . . . . . . . . . 724
7.3.1.3 Federal Water Rights . . . . . . . . . . . . . . . . . . . . . . . . . . 725
7.3.2 U.S. Federal Laws and Permit Requirements . . . . . . . . . . . . . . . . . . 726
7.3.2.1 National Environmental Policy Act (NEPA) . . . . . . . . . . . . . 726
7.3.2.2 Clean Water Act (CWA) . . . . . . . . . . . . . . . . . . . . . . . . 727
7.3.2.3 Rivers and Harbors Act . . . . . . . . . . . . . . . . . . . . . . . . . 729
7.3.2.4 Federal Power Act . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729
7.3.2.5 National Flood Insurance Program . . . . . . . . . . . . . . . . . . . 729
7.3.2.6 Fish and Wildlife Coordination Act . . . . . . . . . . . . . . . . . . 729
7.3.2.7 Migratory Waterfowl Act . . . . . . . . . . . . . . . . . . . . . . . . 729
7.3.2.8 National Wildlife Refuge System Administration Act. . . . . . . . . 730
7.3.2.9 Wild and Scenic Rivers Act . . . . . . . . . . . . . . . . . . . . . . . 730
7.3.2.10 Federal Water Project Recreation Act . . . . . . . . . . . . . . . . . 730
7.3.2.11 Endangered Species Act . . . . . . . . . . . . . . . . . . . . . . . . . 730
7.3.2.12 Safe Drinking Water Act (SDWA) . . . . . . . . . . . . . . . . . . . 730
7.3.2.13 Resource Conservation and Recovery Act (RCRA) . . . . . . . . . . 732
7.3.2.14 Comprehensive Environmental Response, Compensation, and Lia-
bility Act (CERCLA) . . . . . . . . . . . . . . . . . . . . . . . . . . 733
7.3.2.15 Toxic Substance Control Act (TSCA) . . . . . . . . . . . . . . . . . 733
7.3.2.16 Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) . . . . 733
7.3.3 Documentation of Environmental Impacts . . . . . . . . . . . . . . . . . . . . 733
7.3.4 Permit Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735
7.4 Economic Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736
7.4.1 Beneﬁt-Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737
7.4.2 Compound-Interest Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 738

DRAFT as of August 25, 2004 ix
7.4.3 Discounting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740
7.5 Water-Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742
7.5.1 Public-Supply Use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743
7.5.2 Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747
7.5.3 Supply Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749
7.5.3.1 Surface Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 750
7.5.3.2 Ground Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 750
7.5.3.3 Reclaimed Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754
7.5.3.4 Desalination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757
7.6 Floodplain Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757
7.6.1 Modification of the Susceptibility to Flood Damage . . . . . . . . . . . . . . 759
7.6.2 Modification of Flooding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761
7.6.3 Modification of the Impact of Flooding . . . . . . . . . . . . . . . . . . . . . 762
7.7 Droughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762
7.8 Irrigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763
7.9 Dams and Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765
7.10 Hydropower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773
7.11 Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775
A Units and Conversion Factors 241
A.1 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
A.2 Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
B Fluid Properties 245
B.1 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
B.2 Organic Compounds in Found in Water . . . . . . . . . . . . . . . . . . . . . . . . . 246
B.3 Air at Standard Atmospheric Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 248
C Statistical Tables 785
C.1 Areas Under Standard Normal Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 785
C.2 Frequency Factors for Pearson Type III Distribution . . . . . . . . . . . . . . . . . . 788
C.3 Critical Values of the Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . 790
C.4 Critical Values for the Kolmogorov-Smirnov Test Statistic . . . . . . . . . . . . . . . 791
E Special Functions 257
E.1 Error Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
E.2 Bessel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
E.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
E.2.2 Evaluation of Bessel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 259
E.2.2.1 Bessel Function of the First Kind of Order n . . . . . . . . . . . . . 259
E.2.2.2 Bessel Function of the Second Kind of Order n . . . . . . . . . . . . 259
E.2.2.3 Modified Bessel Function of the First Kind of Order n . . . . . . . . 260
E.2.2.4 Modified Bessel Function of the Second Kind of Order n . . . . . . 260
E.2.2.5 Tabulated Values of Useful Bessel Functions . . . . . . . . . . . . . 260
E.3 Gamma Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

x
F Pipe Specifications 801
F.1 PVC Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801
F.2 Ductile Iron Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802
F.3 Concrete Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802
F.4 Physical Properties of Common Pipe Materials . . . . . . . . . . . . . . . . . . . . . 803

Chapter 2
Flow in Closed Conduits
2.1 Introduction
Flow in closed conduits includes all cases where the flowing fluid completely fills the conduit. The
cross-sections of closed conduits can be of any shape or size and can be made of a variety of
materials. Engineering applications of the principles of flow in closed conduits include the design
of municipal water-supply systems and transmission lines. The basic equations governing the flow
of fluids in closed conduits are the continuity, momentum, and energy equations. The most useful
forms of these equations for application to pipe flow problems are derived in this chapter. The
governing equations are presented in forms that are applicable to any fluid flowing in a closed
conduit, but particular attention is given to the flow of water.
The computation of flows in pipe networks is a natural extension of the flows in single pipelines,
and methods of calculating flows and pressure distributions in pipeline systems are also described
here. These methods are particularly applicable to the analysis and design of municipal water
distribution systems, where the engineer is frequently interested in assessing the effects of various
modifications to the system. Because transmission of water in closed conduits is typically accom-
plished using pumps, the fundamentals of pump operation and performance are also presented in
this chapter. A sound understanding of pumps is important in selecting the appropriate pump to
achieve the desired operational characteristics in water transmission systems. The design protocol
for municipal water distribution systems is presented as an example of the application of the prin-
ciples of flow in closed conduits. Methods for estimating water demand, design of the functional
components of distribution systems, network analysis, and the operational criteria for municipal
water distribution systems are all covered.
2.2 Single Pipelines
The governing equations for flows in pipelines are derived from the conservation laws of mass,
momentum, and energy; and the forms of these equations that are most useful for application to
closed-conduit flow are derived in the following sections.
11

12
2.2.1 Continuity Equation
Consider the application of the continuity equation to the control volume illustrated in Figure 2.1.
Fluid enters and leaves the control volume normal to the control surfaces, with the inflow velocity
Flow
Control
volume
Velocity
distribution
Boundary of
control volume
r
v 1
v 2
Figure 2.1: Flow Through Closed Conduit
denoted by v1(r) and the outflow velocity by v2(r). Both the inflow and outflow velocities vary
across the control surface. The steady-state continuity equation for an incompressible fluid can be
written as
A1
v1 dA =

A2
v2 dA (2.1)
Defining V1 and V2 as the average velocities across A1 and A2, respectively, where
V1 =
1
A1

A1
v1 dA (2.2)
and
V2 =
1
A2

A2
v2 dA (2.3)
the steady-state continuity equation becomes
V1A1 = V2A2(= Q) (2.4)
The terms on each side of Equation 2.4 are equal to the volumetric flowrate, Q. The steady-state
continuity equation simply states that the volumetric flowrate across any surface normal to the
flow is a constant.
Example 2.1.
Water enters a pump through a 150-mm diameter intake pipe and leaves the pump through a 200-mm diameter
discharge pipe. If the average velocity in the intake pipeline is 1 m/s, calculate the average velocity in the discharge
pipeline. What is the flowrate through the pump?
Solution.
In the intake pipeline, V1 = 1 m/s, D1 = 0.15 m and
A1 =
π
4
D2
1 =
π
4
(0.15)2
= 0.0177 m2

DRAFT as of August 25, 2004 13
In the discharge pipeline, D2 = 0.20 m and
A2 =
π
4
D2
2 =
π
4
(0.20)2
= 0.0314 m2
According to the continuity equation,
V1A1 = V2A2
Therefore,
V2 = V1

A1
A2

= (1)

0.0177
0.0314

= 0.56 m/s
The flowrate, Q, is given by
Q = A1V1 = (0.0177)(1) = 0.0177 m3
/s
The average velocity in the discharge pipeline is 0.56 m/s, and the flowrate through the pump is 0.0177 m3
/s.
2.2.2 Momentum Equation
Consider the application of the momentum equation to the control volume illustrated in Figure 2.1.
Under steady-state conditions, the component of the momentum equation in the direction of flow
(x-direction) can be written as

Fx =

A
ρvxv · n dA (2.5)
where

Fx is the sum of the x-components of the forces acting on the fluid in the control volume,
ρ is the density of the fluid, vx is the flow velocity in the x-direction, and v · n is the component
of the flow velocity normal to the control surface. Since the unit normal vector, n, in Equation 2.5
is directed outward from the control volume, then the momentum equation for an incompressible
fluid (ρ = constant) can be written as

Fx = ρ

A2
v2
2 dA − ρ

A1
v2
1 dA (2.6)
where the integral terms depend on the velocity distributions across the inflow and outflow control
surfaces. The velocity distribution across each control surface is generally accounted for by the
momentum correction coefficient, β, defined by the relation
β =
1
AV 2

A
v2
dA (2.7)
where A is the area of the control surface and V is the average velocity over the control surface.
The momentum coefficients for the inflow and outflow control surfaces, A1 and A2, are then given
by β1 and β2, where
β1 =
1
A1V 2
1

A1
v2
1 dA (2.8)
β2 =
1
A2V 2
2

A2
v2
2 dA (2.9)
Substituting Equations 2.8 and 2.9 into Equation 2.6 leads to the following form of the momentum
equation
Fx = ρβ2V 2
2 A2 − ρβ1V 2
1 A1 (2.10)

14
Recalling that the continuity equation states that the volumetric flowrate, Q, is the same across
both the inflow and outflow control surfaces, where
Q = V1A1 = V2A2 (2.11)
then combining Equations 2.10 and 2.11 leads to the following form of the momentum equation

Fx = ρβ2QV2 − ρβ1QV1 (2.12)
or
Fx = ρQ(β2V2 − β1V1) (2.13)
In many cases of practical interest, the velocity distribution across the cross-section of the closed
conduit is approximately uniform, in which case the momentum coefficients, β1 and β2, are approx-
imately equal to unity and the momentum equation becomes

Fx = ρQ(V2 − V1) (2.14)
Consider the common case of flow in a straight pipe with a uniform circular cross-section illustrated
in Figure 2.2, where the average velocity remains constant at each cross section,
V1 = V2 = V (2.15)
then the momentum equation becomes
Fx = 0 (2.16)
The forces that act on the fluid in a control volume of uniform cross-section are illustrated in Figure
2.2. At Section 1, the average pressure over the control surface is equal to p1 and the elevation
t0 PL
gAL
Flow
z1
z2
p1
A
A
p2
A
u
1
2
L
Figure 2.2: Forces on Flow in Closed Conduit
of the midpoint of the section relative to a defined datum is equal to z1, at Section 2, located a
distance L downstream from Section 1, the pressure is p2, and the elevation of the midpoint of the
section is z2. The average shear stress exerted on the fluid by the pipe surface is equal to τo, and
the total shear force opposing flow is τoPL, where P is the perimeter of the pipe. The fluid weight
acts vertically downward and is equal to γAL, where γ is the specific weight of the fluid and A is
the cross-sectional area of the pipe. The forces acting on the fluid system that have components
in the direction of flow are the shear force, τoPL; the weight of the fluid in the control volume,

γAL; and the pressure forces on the upstream and downstream faces, p1A and p2A, respectively.
Substituting the expressions for the forces into the momentum equation, Equation 2.16, yields
p1A − p2A − τoPL − γAL sin θ = 0 (2.17)
where θ is the angle that the pipe makes with the horizontal and is given by the relation
sin θ =
z2 − z1
L
(2.18)
Combining Equations 2.17 and 2.18 yields
p1
γ
−
p2
γ
− z2 + z1 =
τoPL
γA
(2.19)
Deﬁning the total head, or energy per unit weight, at Sections 1 and 2 as h1 and h2, where
h1 =
p1
γ
+
V 2
2g
+ z1 (2.20)
and
h2 =
p2
γ
+
V 2
2g
+ z2 (2.21)
then the head loss between Sections 1 and 2, ∆h, is given by
∆h = h1 − h2 =

p1
γ
+ z1

−

p2
γ
+ z2

(2.22)
Combining Equations 2.19 and 2.22 leads to the following expression for head loss
∆h =
τoPL
γA
(2.23)
In this case, the head loss, ∆h, is entirely due to pipe friction and is commonly denoted by hf . In
the case of pipes with circular cross-sections, Equation 2.23 can be written as
hf =
τo(πD)L
γ(πD2/4)
=
4τoL
γD
(2.24)
where D is the diameter of the pipe. The ratio of the cross-sectional area, A, to the perimeter, P,
is deﬁned as the hydraulic radius, R, where
R =
A
P
(2.25)
and the head loss can be written in terms of the hydraulic radius as
hf =
τoL
γR
(2.26)
The form of the momentum equation given by Equation 2.26 is of limited utility in that the head
loss, hf , is expressed in terms of the boundary shear stress, τo, which is not a measurable quantity.

16
However, the boundary shear stress, τo, can be expressed in terms of measurable flow variables using
dimensional analysis, where τo can be taken as a function of the mean flow velocity, V ; density of the
fluid, ρ; dynamic viscosity of the fluid, µ; diameter of the pipe, D; characteristic size of roughness
projections, ; characteristic spacing of the roughness projections, ; and a (dimensionless) form
factor, m, that depends on the shape of the roughness elements on the surface of the conduit. This
functional relationship can be expressed as
τo = f1(V, ρ, µ, D, ,
, m) (2.27)
According to the Buckingham pi theorem, this relationship between eight variables in three fun-
damental dimensions can also be expressed as a relationship between five nondimensional groups.
The following relation is proposed
τo
ρV 2
= f2

Re,

D
,

D
, m

(2.28)
where Re is the Reynolds number defined by
Re =
ρV D
µ
(2.29)
The relationship given by Equation 2.28 is as far as dimensional analysis goes, and experiments
are necessary to determine an empirical relationship between the nondimensional groups. Nikuradse
(1932; 1933) conducted a series of experiments in pipes in which the inner surfaces were roughened
with sand grains of uniform diameter, . In these experiments, the spacing, , and shape, m, of
the roughness elements (sand grains) were constant and Nikuradse’s experimental data fitted to
the following functional relation
τo
ρV 2
= f3

Re,

D

(2.30)
It is convenient for subsequent analysis to introduce a factor of 8 into this relationship, which can
then be written as
τo
ρV 2
=
1
8
f

Re,

D

(2.31)
or simply
τo
ρV 2
=
f
8
(2.32)
where the dependence of the friction factor, f, on the Reynolds number, Re, and relative rough-
ness, /D, is understood. Combining Equations 2.32 and 2.24 leads to the following form of the
momentum equation for flows in circular pipes
hf =
fL
D
V 2
2g
(2.33)
This equation, called the Darcy-Weisbach equation,∗ expresses the frictional head loss, hf , of the
fluid over a length L of pipe in terms of measurable parameters, including the pipe diameter (D),
∗
Henry Darcy (1803–1858) was a nineteenth-century French engineer; Julius Weisbach (1806 – 1871) was a German
engineer of the same era. Weisbach proposed the use of a dimensionless resistance coefficient, and Darcy carried out
the tests on water pipes.

average flow velocity (V ), and the friction factor (f) that characterizes the shear stress of the fluid
on the pipe. Some references name Equation 2.33 simply as the Darcy equation, however this is
inappropriate since it was Julius Weisbach who first proposed the exact form of Equation 2.33 in
1845, with Darcy’s contribution on the functional dependence of f on V and D in 1857 (Brown,
2002; Rouse and Ince, 1957). The occurrence and differences between laminar and turbulent flow
was later quantified by Osbourne Reynolds† in 1883 (Reynolds, 1883).
Based on Nikuradse’s (1932, 1933) experiments on sand-roughened pipes, Prandl and von
Kármán established the following empirical formulae for estimating the friction factor in turbu-
lent pipe flows
Smooth pipe

k
D ≈ 0

: 1
√
f
= −2 log

2.51
Re
√
f

Rough pipe

k
D 0

: 1
√
f
= −2 log

k/D
3.7

(2.34)
where k is the roughness height of the sand grains on the surface of the pipe. Turbulent flow in
pipes is generally present when Re 4,000; transition to turbulent flow begins at about Re = 2,300.
The pipe behaves like a smooth pipe when the friction factor does not depend on the height of the
roughness projections on the wall of the pipe and therefore depends only on the Reynolds number.
In rough pipes, the friction factor is determined by the relative roughness, k/D, and becomes
independent of the Reynolds number. The smooth pipe case generally occurs at lower Reynolds
numbers, when the roughness projections are submerged within the viscous boundary layer. At
higher values of the Reynolds number, the thickness of the viscous boundary layer decreases and
eventually the roughness projections protrude sufficiently far outside the viscous boundary layer
that the shear stress of the pipe boundary is dominated by the hydrodynamic drag associated with
the roughness projections into the main body of the flow. Under these circumstances, the flow
in the pipe becomes fully turbulent, the friction factor is independent of the Reynolds number,
and the pipe is considered to be (hydraulically) rough. The flow is actually turbulent under both
smooth-pipe and rough-pipe conditions, but the flow is termed fully turbulent when the friction
factor is independent of the Reynolds number. Between the smooth- and rough-pipe conditions,
there is a transition region in which the friction factor depends on both the Reynolds number and
the relative roughness. Colebrook (1939) developed the following relationship that asymptotes to
the Prandl and von Kármán relations
1
√
f
= −2 log

k/D
3.7
+
2.51
Re
√
f

(2.35)
This equation is commonly referred to as the Colebrook equation orColebrook-White equation.
Equation 2.35 can be applied in the transition region between smooth-pipe and rough-pipe condi-
tions, and values of friction factor, f, predicted by the Colebrook equation are generally accurate
to within 10–15% of experimental data (Finnemore and Franzini, 2002; Alexandrou, 2001).
Commercial pipes differ from Nikuradse’s experimental pipes in that the heights of the roughness
projections are not uniform and are not uniformly distributed. In commercial pipes, an equivalent
sand roughness, ks, is defined as the diameter of Nikuradse’s sand grains that would cause the same
head loss as in the commercial pipe. The equivalent sand roughness, ks, of several commercial pipe
materials are given in Table 2.1. These values of ks apply to clean new pipe only; pipe that has been
†
Osbourne Reynolds (1842 to 1912).

18
Table 2.1: Typical Equivalent Sand Roughness for Various New Materials
Equivalent sand
roughness, ks
Material (mm)
Asbestos cement:
Coated 0.038
Uncoated 0.076
Brass 0.0015–0.003
Brick 0.6
Concrete:
General 0.3–3.0
Steel forms 0.18
Wooden forms 0.6
Centrifugally spun 0.13–0.36
Copper 0.0015–0.003
Corrugated metal 45
Glass 0.0015–0.003
Iron:
Cast iron 0.19–0.26
Ductile iron:
Lined with bitumen 0.12–0.03
Lined with spun concrete 0.030–038
Galvanized iron 0.013–0.15
Wrought iron 0.046 – 0.06
Lead 0.0015
Plastic (PVC) 0.0015–0.03
Steel
Coal-tar enamel 0.0048
New unlined 0.045–0.076
Riveted 0.9–9.0
Wood stave 0.18
Sources: Haestad Methods, Inc. (2002), Moody (1944), Sanks (1998)).

in service for a long time usually experiences corrosion or scale buildup that results in values of ks
that are orders of magnitude larger than the values given in Table 2.1 (Echávez, 1997; Gerhart et
al., 1992). The rate of increase of ks with time depends primarily on the quality of the water being
transported, and the roughness coefficients for older water mains are usually determined through
field testing (AWWA, 1992). The expression for the friction factor derived by Colebrook (Equation
2.35) was plotted by Moody (1944) in what is today commonly referred to as the Moody diagram,∗
reproduced in Figure 2.3. The Moody diagram indicates that for Re ≤ 2,000, the flow is laminar
64
Re
f 5
Rough turbulent zone
Transitional zone
103
104
Reynolds number, Re
1
0.038
Friction
factor,
f
0.002
Relative
roughness,
k
s
/D
2 3 4 5 6 7891
105
2 3 4 5 6 7891
106
2 3 4 5 6 7891
107
2 3 4 2 3 4
5 6 7891
0.036
0.034
0.032
0.030
0.028
0.026
0.024
0.022
0.020
0.018
0.016
0.014
0.012
0.010
0.008
0.001
0.0006
0.0004
0.0002
0.0001
0.00005
0.00001
0.004
0.006
0.008
0.01
Laminar flow
Smooth pipes
Figure 2.3: Moody Diagram
Source: Moody, L. F. “Friction Factors for Pipe Flow” 66(8), 1944, ASME, New York.
and the friction factor is given by
f =
64
Re
(2.36)
which can be derived theoretically based on the assumption of laminar flow of a Newtonian fluid
(Daily and Harleman, 1966). For 2000 Re ≤ 4000 there is no fixed relationship between the
friction factor and the Reynolds number or relative roughness, and flow conditions are generally
uncertain (Wilkes, 1999). Beyond a Reynolds number of 4000, the flow is turbulent and the friction
∗
This type of diagram was originally suggested by Blasius in 1913 and Stanton in 1914 (Stanton and Pannell,
1914). The Moody diagram is sometimes called the Stanton diagram (Finnemore and Franzini (2002).

20
factor is controlled by the thickness of the laminar boundary layer relative to the height of the
roughness projections on the surface of the pipe. The dashed line in Figure 2.3 indicates the
boundary between the fully turbulent flow regime, where f is independent of Re, and the transition
regime, where f depends on both Re and the relative roughness, ks/D. The equation of this dashed
line is given by Mott (1994) as
1
√
f
=
Re
200(D/ks)
(2.37)
The line in the Moody diagram corresponding to a relative roughness of zero describes the friction
factor for pipes that are hydraulically smooth.
Although the Colebrook equation (Equation 2.35) can be used to calculate the friction factor
in lieu of the Moody diagram, this equation has the drawback that it is an implicit equation for
the friction factor and must be solved iteratively. This minor inconvenience was circumvented by
Jain (1976), who suggested the following explicit equation for the friction factor
1
√
f
= −2 log

ks/D
3.7
+
5.74
Re0.9

, 10−6
≤
ks
D
≤ 10−2
, 5,000 ≤ Re ≤ 108
(2.38)
where, according to Jain (1976), Equation 2.38 deviates by less than 1% from the Colebrook
equation within the entire turbulent flow regime, provided that the restrictions on ks/D and Re are
honored. According to Franzini and Finnemore (1997) and Granger (1985), values of the friction
factor calculated using the Colebrook equation are generally accurate to within 10% to 15% of
experimental data, while Potter and Wiggert (2001) put the accuracy of the Moody diagram at no
more than 5%. The Jain equation (Equation 2.38) can be more conveniently written as
f =
0.25

log

ks
3.7D + 5.74
Re0.9
2 , 10−6
≤
ks
D
≤ 10−2
, 5,000 ≤ Re ≤ 108
(2.39)
Uncertainties in relative roughness and in the data used to produce the Colebrook equation make
the use of several-place accuracy in pipe flow problems unjustified. As a rule of thumb, an accuracy
of 10% in calculating friction losses in pipes is to be expected (Munson et al., 1994; Gerhart et al.,
1992).
Example 2.2.
Water from a treatment plant is pumped into a distribution system at a rate of 4.38 m3
/s, a pressure of 480 kPa,
and a temperature of 20◦
C. The diameter of the pipe is 750 mm and is made of ductile iron. Estimate the pressure
200 m downstream of the treatment plant if the pipeline remains horizontal. Compare the friction factor estimated
using the Colebrook equation to the friction factor estimated using the Jain equation. After 20 years in operation,
scale buildup is expected to cause the equivalent sand roughness of the pipe to increase by a factor of 10. Determine
the effect on the water pressure 200 m downstream of the treatment plant.
Solution.
According to the Darcy-Weisbach equation, the difference in total head, ∆h, between the upstream section (at exit
from treatment plant) and the downstream section (200 m downstream from the upstream section) is given by
∆h =
fL
D
V 2
2g
where f is the friction factor, L is the pipe length between the upstream and downstream sections (= 200 m), D is
the pipe diameter (= 750 mm), and V is the velocity in the pipe. The velocity, V , is given by
V =
Q
A

where Q is the flowrate in the pipe (= 4.38 m3
/s) and A is the area of the pipe cross-section given by
A =
π
4
D2
=
π
4
(0.75)2
= 0.442 m2
The pipeline velocity is therefore
V =
Q
A
=
4.38
0.442
= 9.91 m/s
The friction factor, f, in the Darcy-Weisbach equation is calculated using the Colebrook equation
1
√
f
= −2 log

ks
3.7D
+
2.51
Re
√
f

where Re is the Reynolds number and ks is the equivalent sand roughness of ductile iron (= 0.26 mm). The Reynolds
number is given by
Re =
V D
ν
where ν is the kinematic viscosity of water at 20◦
C, which is equal to 1.00 × 10−6
m2
/s. Therefore
Re =
V D
ν
=
(9.91)(0.75)
1.00 × 10−6
= 7.43 × 106
Substituting into the Colebrook equation leads to
1
√
f
= −2 log

0.26
(3.7)(750)
+
2.51
7.43 × 106
√
f

or
1
√
f
= −2 log

9.37 × 10−5
+
3.38 × 10−7
√
f

This is an implicit equation for f, and by trial and error the solution is
f = 0.016
The head loss, ∆h, between the upstream and downstream sections can now be calculated using the Darcy-Weisbach
equation as
∆h =
fL
D
V 2
2g
=
(0.016)(200)
0.75
(9.91)2
(2)(9.81)
= 21.4 m
Using the definition of head loss, ∆h,
∆h =

p1
γ
+ z1

−

p2
γ
+ z2

where p1 and p2 are the upstream and downstream pressures, γ is the specific weight of water, and z1 and z2 are the
upstream and downstream pipe elevations. Since the pipe is horizontal, z1 = z2 and ∆h can be written in terms of
the pressures at the upstream and downstream sections as
∆h =
p1
γ
−
p2
γ
In this case, p1 = 480 kPa, γ = 9.79 kN/m3
, and therefore
21.4 =
480
9.79
−
p2
9.79
which yields
p2 = 270 kPa
Therefore, the pressure 200 m downstream of the treatment plant is 270 kPa. The Colebrook equation required that
f be determined iteratively, but the explicit Jain approximation for f is given by
1
√
f
= −2 log

ks
3.7D
+
5.74
Re0.9

22
Substituting for ks, D, and Re gives
1
√
f
= −2 log

0.26
(3.7)(750)
+
5.74
(7.43 × 106)0.9

which leads to
f = 0.016
This is the same friction factor obtained using the Colebrook equation within an accuracy of two significant digits.
After 20 years, the equivalent sand roughness, ks, of the pipe is 2.6 mm, the (previously calculated) Reynolds
number is 7.43 × 106
, and the Colebrook equation gives
1
√
f
= −2 log

2.6
(3.7)(750)
+
2.51
7.43 × 106
√
f

or
1
√
f
= −2 log

9.37 × 10−4
+
3.38 × 10−7
√
f

which yields
f = 0.027
The head loss, ∆h, between the upstream and downstream sections is given by the Darcy-Weisbach equation as
∆h =
fL
D
V 2
2g
=
(0.027)(200)
0.75
(9.91)2
(2)(9.81)
= 36.0 m
Hence the pressure, p2, 200 m downstream of the treatment plant is given by the relation
∆h =
p1
γ
−
p2
γ
where p1 = 480 kPa, γ = 9.79 kN/m3
, and therefore
36.0 =
480
9.79
−
p2
9.79
which yields
p2 = 128 kPa
Therefore, pipe aging over 20 years will cause the pressure 200 m downstream of the treatment plant to decrease
from 270 kPa to 128 kPa. This is quite a significant drop and shows why velocities of 9.91 m/s are not used in these
pipelines, even for short lengths of pipe.
The problem in Example 3.2 illustrates the case where the flowrate through a pipe is known
and the objective is to calculate the head loss and pressure drop over a given length of pipe.
The approach is summarized as follows: (1) calculate the Reynolds number, Re, and the relative
roughness, ks/D, from the given data; (2) use the Colebrook equation (Equation 2.35) or Jain
equation (Equation 2.38) to calculate f; and (3) use the calculated value of f to calculate the head
loss from the Darcy-Weisbach equation (Equation 2.33), and the corresponding pressure drop from
Equation 2.22.
Flowrate for a Given Head Loss. In many cases, the flowrate through a pipe is not controlled
but attains a level that matches the pressure drop available. For example, the flowrate through
faucets in home plumbing is determined by the gage pressure in the water main, which is relatively
insensitive to the flow through the faucet. A useful approach to this problem that utilizes the

Colebrook equation has been suggested by Fay (1994), where the ﬁrst step is to calculate Re
√
f
using the rearranged Darcy-Weisbach equation
Re

f =

2ghf D3
ν2L
1
2
(2.40)
Using this value of Re
√
f, solve for Re using the rearranged Colebrook equation
Re = −2.0(Re

f) log

ks/D
3.7
+
2.51
Re
√
f

(2.41)
Using this value of Re, the ﬂowrate, Q, can then be calculated by
Q =
1
4
πD2
V =
1
4
πDνRe (2.42)
This approach must necessarily be validated by verifying that Re 2,300, which is required for the
application of the Colebrook equation. Swamee and Jain (1976) combine Equations 2.40 to 2.42 to
yield
Q = −0.965D2

gDhf
L
ln
⎛
⎝
ks/D
3.7
+
1.784ν
D

gDhf /L
⎞
⎠ (2.43)
Example 2.3.
A 50-mm diameter galvanized iron service pipe is connected to a water main in which the pressure is 450 kPa gage.
If the length of the service pipe to a faucet is 40 m and the faucet is 1.2 m above the main, estimate the ﬂowrate
when the faucet is fully open.
Solution.
The head loss, hf , in the pipe is estimated by
hf =

pmain
γ
+ zmain

−

poutlet
γ
+ zoutlet

where pmain = 450 kPa, zmain = 0 m, poutlet = 0 kPa, and zoutlet = 1.2 m. Therefore, taking γ = 9.79 kn/m3
(at
20◦
C) gives
hf =

450
9.79
+ 0

− (0 + 1.2) = 44.8 m
Also, since D = 50 mm, L = 40 m, ks = 0.15 mm (from Table 2.1), ν = 1.00×10−6
m2
/s (at 20◦
C), the Swamee-Jain
equation (Equation 2.43) yields
Q = −0.965D2

gDhf
L
ln

ks/D
3.7
+
1.784ν
D

gDhf /L

= −0.965(0.05)2

(9.81)(0.05)(44.8)
40
ln

0.15/50
3.7
+
1.784(1.00 × 10−6
)
(0.05)

(9.81)(0.05)(44.8)/40

= 0.0126 m3
/s = 12.6 L/s
The faucet can therefore be expected to deliver 12.6 L/s when fully open.

24
Diameter for a Given Flowrate and Head Loss. In many cases, an engineer must select a
size of pipe to provide a given level of service. For example, the maximum flowrate and maximum
allowable pressure drop may be specified for a water delivery pipe, and the engineer is required to
calculate the minimum diameter pipe that will satisfy these design constraints. Solution of this
problem necessarily requires an iterative procedure. Streeter and Wylie (1985) have suggested the
following steps
1. Assume a value of f.
2. Calculate D from the rearranged Darcy-Weisbach equation,
D = 5

8LQ2
hf gπ2
f

(2.44)
where the term in parentheses can be calculated from given data.
3. Calculate Re from
Re =
V D
ν
=

4Q
πν

1
D
(2.45)
where the term in parentheses can be calculated from given data.
4. Calculate ks/D.
5. Use Re and ks/D to calculate f from the Colebrook equation.
6. Using the new f, repeat the procedure until the new f agrees with the old f to the first two
significant digits.
Example 2.4.
A galvanized iron service pipe from a water main is required to deliver 200 L/s during a fire. If the length of the service
pipe is 35 m and the head loss in the pipe is not to exceed 50 m, calculate the minimum pipe diameter that can be used.
Solution.
Step 1: Assume f = 0.03
Step 2: Since Q = 0.2 m3
/s, L = 35 m, and hf = 50 m, then
D = 5

8LQ2
hf gπ2

f = 5

8(35)(0.2)2
(50)(9.81)π2

(0.03) = 0.147 m
Step 3: Since ν = 1.00 × 10−6
m2
/s (at 20◦
C), then
Re =

4Q
πν

1
D
=

4(0.2)
π(1.00 × 10−6)

1
0.147
= 1.73 × 106
Step 4: Since ks = 0.15 mm (from Table 2.1, for new pipe), then
ks
D
=
1.5 × 10−4
0.147
= 0.00102

Step 5: Using the Colebrook equation (Equation 2.35) gives
1
√
f
= −2 log

ks/D
3.7
+
2.51
Re
√
f

= −2 log

0.00102
3.7
+
2.51
1.73 × 106
√
f

which leads to
f = 0.020
Step 6: f = 0.020 differs from the assumed f (= 0.03), so repeat the procedure with f = 0.020.
Step 2: For f = 0.020, D = 0.136 m
Step 3: For D = 0.136, Re = 1.87 × 106
Step 4: For D = 0.136, ks/D = 0.00110
Step 5: f = 0.020
Step 6: The calculated f (= 0.020) is equal to the assumed f. The required pipe diameter is therefore equal to 0.136
m or 136 mm. A commercially available pipe with the closest diameter larger than 136 mm should be used.
The iterative procedure demonstrated in the previous example converges fairly quickly, and
does not pose any computational difficulty. Swamee and Jain (1976) have suggested the following
explicit formula for calculating the pipe diameter, D,
D = 0.66
⎡
⎣k1.25
s

LQ2
ghf
4.75
+ νQ9.4

L
ghf
5.2
⎤
⎦
0.04
,
3,000 ≤ Re ≤ 3 × 108
, 10−6
≤
ks
D
≤ 2 × 10−2
(2.46)
Equation 2.46 will yield a D within 5% of the value obtained by the method using the Colebrook
equation. This method is illustrated by repeating the previous example.
Example 2.5.
A galvanized iron service pipe from a water main is required to deliver 200 L/s during a fire. If the length of the
service pipe is 35 m, and the head loss in the pipe is not to exceed 50 m, use the Swamee-Jain equation to calculate
the minimum pipe diameter that can be used.
Solution.
Since ks = 0.15 mm, L = 35 m, Q = 0.2 m3
/s, hf = 50 m, ν = 1.00 × 10−6
m2
/s, the Swamee-Jain equation gives
D = 0.66

k1.25
s

LQ2
ghf
4.75
+ νQ9.4

L
ghf
5.2
0.04
= 0.66

(0.00015)1.25

(35)(0.2)2
(9.81)(50)
4.75
+ (1.00 × 10−6
)(0.2)9.4

35
(9.81)(50)
5.2 0.04
= 0.140 m
The calculated pipe diameter (140 mm) is about 3% higher than calculated by the Colebrook equation (136 mm).
2.2.3 Energy Equation
The steady-state energy equation for the control volume illustrated in Figure 2.4 is given by

26
Shaft work, Ws
Control
volume
Heat flux, Qh
Inflow, Q Outflow, Q
2
1
Figure 2.4: Energy Balance in Closed Conduit
dQh
dt
−
dW
dt
=

A
ρe v · n dA (2.47)
where Qh is the heat added to the fluid in the control volume, W is the work done by the fluid in
the control volume, A is the surface area of the control volume, ρ is the density of the fluid in the
control volume, and e is the internal energy per unit mass of fluid in the control volume given by
e = gz +
v2
2
+ u (2.48)
where z is the elevation of the fluid mass having a velocity v and internal energy u. By convention,
the heat added to a system and the work done by a system are positive quantities. The normal
stresses on the inflow and outflow boundaries of the control volume are equal to the pressure, p,
with shear stresses tangential to the boundaries of the control volume. As the fluid moves across
the control surface with velocity v, the power (= rate of doing work) expended by the fluid against
the external pressure forces is given by
dWp
dt
=

A
pv · n dA (2.49)
where Wp is the work done against external pressure forces. The work done by a fluid in the control
volume is typically separated into work done against external pressure forces, Wp, plus work done
against rotating surfaces, Ws, commonly referred to as the shaft work. The rotating element is
called a rotor in a gas or steam turbine, an impeller in a pump, and a runner in a hydraulic
turbine. The rate at which work is done by a fluid system, dW/dt, can therefore be written as
dW
dt
=
dWp
dt
+
dWs
dt
=

A
pv · n dA +
dWs
dt
(2.50)
Combining Equation 2.50 with the steady-state energy equation (Equation 2.47) leads to
dQh
dt
−
dWs
dt
=

A
ρ

p
ρ
+ e

v · n dA (2.51)
Substituting the definition of the internal energy, e, given by Equation 2.48 into Equation 2.51
yields
dQh
dt
−
dWs
dt
=

A
ρ

h + gz +
v2
2

v · n dA (2.52)

where h is the enthalpy of the fluid defined by
h =
p
ρ
+ u (2.53)
Denoting the rate at which heat is being added to the fluid system by Q̇, and the rate at which
work is being done against moving impervious boundaries (shaft work) by Ẇs, then the energy
equation can be written in the form
Q̇ − Ẇs =

A
ρ

h + gz +
v2
2

v · n dA (2.54)
Considering the terms h + gz, where
h + gz =
p
ρ
+ u + gz = g

p
γ
+ z

+ u (2.55)
and γ is the specific weight of the fluid, then Equation 2.55 indicates that h + gz can be assumed
to be constant across the inflow and outflow openings illustrated in Figure 2.4, since a hydrostatic
pressure distribution across the inflow/outflow boundaries guarantees that p/γ+z is constant across
the inflow/outflow boundaries normal to the flow direction, and the internal energy, u, depends
only on the temperature, which can be assumed constant across each boundary. Since v · n is
equal to zero over the impervious boundaries in contact with the fluid system, Equation 2.54 can
be integrated to yield
Q̇ − Ẇs = (h1 + gz1)

A1
ρv · n dA +

A1
ρ
v2
2
v · n dA + (h2 + gz2)

A2
ρv · n dA
+

A2
ρ
v2
2
v · n dA
= −(h1 + gz1)

A1
ρv1 dA −

A1
ρ
v3
1
2
dA + (h2 + gz2)

A2
ρv2 dA
+

A2
ρ
v3
2
2
dA (2.56)
where the subscripts 1 and 2 refer to the inflow and outflow boundaries, respectively, and the
negative signs result from the fact that the unit normal points out of the control volume, causing
v · n to be negative on the inflow boundary and positive on the outflow boundary.
Equation 2.56 can be simplified by noting that the assumption of steady flow requires that rate
of mass inflow to the control volume is equal to the mass outflow rate and, denoting the mass flow
rate by ṁ, the continuity equation requires that
ṁ =

A1
ρv1 dA =

A2
ρv2 dA (2.57)
Furthermore, the constants α1 and α2 can be defined by the equations

A1
ρ
v3
2
dA = α1ρ
V 3
1
2
A1 (2.58)

A2
ρ
v3
2
dA = α2ρ
V 3
2
2
A2 (2.59)

28
where A1 and A2 are the areas of the inflow and outflow boundaries, respectively, and V1 and
V2 are the corresponding mean velocities across these boundaries. The constants α1 and α2 are
determined by the velocity profile across the flow boundaries, and these constants are called kinetic
energy correction factors. If the velocity is constant across a flow boundary, then it is clear from
Equation 2.58 that the kinetic energy correction factor for that boundary is equal to unity; for any
other velocity distribution, the kinetic energy factor is greater than unity. Combining Equations
2.56 to 2.59 leads to
Q̇ − Ẇs = −(h1 + gz1)ṁ − α1ρ
V 3
1
2
A1 + (h2 + gz2)ṁ + α2ρ
V 3
2
2
A2 (2.60)
Invoking the continuity equation requires that
ρV1A1 = ρV2A2 = ṁ (2.61)
and combining Equations 2.60 and 2.61 leads to
Q̇ − Ẇs = ṁ

h2 + gz2 + α2
V 2
2
2

−

h1 + gz1 + α1
V 2
1
2

(2.62)
which can be put in the form
Q̇
ṁg
−
Ẇs
ṁg
=

p2
γ
+
u2
g
+ z2 + α2
V 2
2
2g

−

p1
γ
+
u1
g
+ z1 + α1
V 2
1
2g

(2.63)
and can be further rearranged into the useful form

p1
γ
+ α1
V 2
1
2g
+ z1

=

p2
γ
+ α2
V 2
2
2g
+ z2

+

1
g
(u2 − u1) −
Q̇
ṁg

+

Ẇs
ṁg

(2.64)
Two key terms can be identified in Equation 2.64: the (shaft) work done by the fluid per unit
weight, hs, defined by the relation
hs =
Ẇs
ṁg
(2.65)
and the energy loss per unit weight, commonly called the head loss, hL, defined by the relation
hL =
1
g
(u2 − u1) −
Q̇
ṁg
(2.66)
Combining Equations 2.64 to 2.66 leads to the most common form of the energy equation

p1
γ
+ α1
V 2
1
2g
+ z1

=

p2
γ
+ α2
V 2
2
2g
+ z2

+ hL + hs (2.67)
where a positive head loss indicates an increase in internal energy, manifested by an increase in
temperature or a loss of heat, and a positive value of hs is associated with work being done by the
fluid, such as in moving a turbine runner. Many practitioners incorrectly refer to Equation 2.67 as
the Bernoulli equation, which bears some resemblance to Equation 2.67 but is different in several
important respects. Fundamental differences between the energy equation and the Bernoulli equa-
tion are that the Bernoulli equation is derived from the momentum equation, which is independent
of the energy equation, and the Bernoulli equation does not account for fluid friction.

Energy and Hydraulic Grade Lines. The total head, h, of a fluid at any cross-section of a
pipe is defined by
h =
p
γ
+ α
V 2
2g
+ z (2.68)
where p is the pressure in the fluid at the centroid of the cross-section, γ is the specific weight of
the fluid, α is the kinetic energy correction factor, V is the average velocity across the pipe, and z
is the elevation of the centroid of the pipe. The total head measures the average energy per unit
weight of the fluid flowing across a pipe cross-section. The energy equation, Equation 2.67, states
that changes in the total head along the pipe are described by
h(x + ∆x) = h(x) − (hL + hs) (2.69)
where x is the coordinate measured along the pipe centerline, ∆x is the distance between two
cross-sections in the pipe, hL is the head loss, and hs is the shaft work done by the fluid over the
distance ∆x. The practical application of Equation 2.69 is illustrated in Figure 2.5, where the head
loss, hL, between two sections a distance ∆x apart is indicated. At each cross-section, the total
Dx
2
1
Q
Q
z2
z1
Head loss, hL
Energy grade line (EGL)
Hydraulic grade line (HGL)
Datum
2g
a1
V 1
2
2g
a2
V 2
2
g
p
2
g
p
1
Figure 2.5: Head Loss Along Pipe
energy, h, is plotted relative to a defined datum, and the locus of these points is called the energy
grade line. The energy grade line at each pipe cross-section is located a distance p/γ + αV 2/2g
vertically above the centroid of the cross-section, and between any two cross-sections the elevation
of the energy grade line falls by a vertical distance equal to the head loss caused by pipe friction,
hL, plus the shaft work, hs, done by the fluid. The hydraulic grade line measures the hydraulic
head p/γ + z at each pipe cross-section. It is located a distance p/γ above the pipe centerline and
indicates the elevation to which the fluid would rise in an open tube connected to the wall of the

30
pipe section. The hydraulic grade line is therefore located a distance αV 2/2g below the energy
grade line. In most water-supply applications the velocity heads are negligible and the hydraulic
grade line closely approximates the energy grade line.
Both the hydraulic grade line and the energy grade line are useful in visualizing the state of
the fluid as it flows along the pipe and are frequently used in assessing the performance of fluid
delivery systems. Most fluid delivery systems, for example, require that the fluid pressure remain
positive, in which case the hydraulic grade line must remain above the pipe. In circumstances where
additional energy is required to maintain acceptable pressures in pipelines, a pump is installed along
the pipeline to elevate the energy grade line by an amount hs, which also elevates the hydraulic
grade line by the same amount. This condition is illustrated in Figure 2.6. In cases where the
Dx
2
1
Pump
X
z2
z1
hs
Energy grade line (EGL)
Hydraulic grade line (HGL)
Datum
2g
a1
V 1
2
2g
a2
V 2
2
g
p2
g
p1
Figure 2.6: Pump Effect on Flow in Pipeline
pipeline upstream and downstream of the pump are of the same diameter, then the velocity heads
αV 2/2g both upstream and downstream of the pump are the same, and the head added by the
pump, hs, goes entirely to increase the pressure head, p/γ, of the fluid. It should also be clear from
Figure 2.5 that the pressure head in a pipeline can be increased by simply increasing the pipeline
diameter, which reduces the velocity head, αV 2/2g, and thereby increases the pressure head, p/γ,
to maintain the same total energy at the pipe section.
Velocity Profile. The momentum and energy correction factors, α and β, depend on the cross-
sectional velocity distribution. The velocity profile in both smooth and rough pipes of circular
cross-section can be estimated by the semi-empirical equation
v(r) =

(1 + 1.326

where v(r) is the velocity at a radial distance r from the centerline of the pipe, R is the radius of
the pipe, f is the friction factor, and V is the average velocity across the pipe.
The velocity distribution given by Equation 2.70 agrees well with velocity measurements in both
smooth and rough pipes. This equation, however, is not applicable within the small region close to
the centerline of the pipe and is also not applicable in the small region close to the pipe boundary.
This is apparent since at the axis of the pipe dv/dr must be equal to zero, but Equation 2.70 does
not have a zero slope at r = 0. The pipe boundary v must also be equal to zero, but Equation 2.70
gives a velocity of zero at a small distance from the wall, with a velocity of −∞ at r = R. The
energy and momentum correction factors, α and β, derived from the velocity profile are (Moody,
1950)
α = 1 + 2.7f (2.71)
β = 1 + 0.98f (2.72)
Another commonly used equation to describe the velocity distribution in turbulent pipe flow is
the empirical power law equation given by
v(r) = Vo

1 −
r
R
1
n
(2.73)
where Vo is the centerline velocity and n is a function of the Reynolds number, Re. Values of n typ-
ically range between 6 and 10 and can be approximated by (Fox and McDonald, 1992; Schlichting,
1979)
n = 1.83 log Re − 1.86 (2.74)
The power law is not applicable within 0.04R of the wall, since the power law gives an infinite
velocity gradient at the wall. Although the profile fits the data close to the centerline of the pipe,
it does not give zero slope at the centerline. The kinetic energy coefficient, α, derived from the
power law equation is given by
α =
(1 + n)3(1 + 2n)3
4n4(3 + n)(3 + 2n)
(2.75)
For n between 6 and 10, α varies from 1.08 to 1.03. In most engineering applications, α and β are
taken as unity (see Problem 2.14).
Head Losses in Transitions and Fittings. The head losses in straight pipes of constant
diameter are caused by friction between the moving fluid and the pipe boundary and are estimated
using the Darcy-Weisbach equation. Flow through pipe fittings, around bends, and through changes
in pipeline geometry cause additional head losses, ho, that are quantified by an equation of the form
ho =

K
V 2
2g
(2.76)
where K is a loss coefficient that is specific to each fitting and transition and V is the average ve-
locity at a defined location within the transition or fitting. The loss coefficients for several fittings
and transitions are shown in Figure 2.7. Head losses in transitions and fittings are also called local
head losses or minor head losses. The latter term should be avoided, however, since in some cases

32
D2/D1
V2
D2
u
d V
r
D1
r
Vanes
Description
Pipe entrance
Sketch Additional Data K
r /d
K
K 5 1.1
1
2
4
6
r /d
0.0
0.1
0.2
0.50
0.12
0.03
Contraction
Expansion
90° miter bend
90° smooth bend
Threaded
pipe fittings
K
0.0
0.20
0.40
0.60
0.80
0.90
0.08
0.08
0.07
0.06
0.06
0.06
V1 D u
d
D2
u 5 60°
K
0.50
0.49
0.42
0.27
0.20
0.10
u 5 180°
K
0.35
0.19
0.16
0.21
K
10.0
5.0
0.2
5.6
2.2
0.4
1.8
0.9
0.4
Globe valve — wide open
Angle valve — wide open
Gate valve — wide open
Gate valve — half open
Return bend
Tee
straight-through flow
side-outlet flow
90° elbow
45° elbow
u 5 90°
D1/D2 K
0.0
0.20
0.40
0.60
0.80
Without
vanes
0.30
0.25
0.15
0.10
u 5 20°
K
1.00
0.87
0.70
0.41
0.15
u 5 180°
K 5 0.2
With
vanes
Figure 2.7: Loss Coeﬃcients for Transitions and Fittings
Source: Roberson, John A. and Crowe, Clayton T., Engineering Fluid Mechanics. Copyright c
1997 by John Wiley
Sons, Inc. Reprinted by permission of John Wiley Sons, Inc.

these head losses are a significant portion of the total head loss in a pipe. Detailed descriptions of
local head losses in various valve geometries can be found in Mott (1994), and additional data on
local head losses in pipeline systems can be found in Brater and colleagues (1996).
Example 2.6.
A pump is to be selected that will pump water from a well into a storage reservoir. In order to fill the reservoir in a
timely manner, the pump is required to deliver 5 L/s when the water level in the reservoir is 5 m above the water level
in the well. Find the head that must be added by the pump. The pipeline system is shown in Figure 2.8. Assume
Reservoir
5 m
5 m 5 m
100 mm PVC (pump to reservoir)
15 m
P
2 m
3 m
50 mm PVC (well to pump)
Well
Figure 2.8: Pipeline System
that the minor loss coefficient for each of the bends is equal to 0.25 and that the temperature of the water is 20◦
C.
Solution.
Taking the elevation of the water surface in the well to be equal to 0 m, and proceeding from the well to the storage
reservoir (where the head is equal to 5 m), the energy equation (Equation 2.67) can be written as
0 −
V 2
1
2g
−
f1L1
D1
V 2
1
2g
− K1
V 2
1
2g
+ hp −
f2L2
D2
V 2
2
2g
− (K2 + K3)
V 2
2
2g
−
V 2
2
2g
= 5
where V1 and V2 are the velocities in the 50-mm (= D1) and 100-mm (= D2) pipes, respectively; L1 and L2 are the
corresponding pipe lengths; f1 and f2 are the corresponding friction factors; K1, K2, and K3 are the loss coefficients
for each of the three bends; and hp is the head added by the pump. The cross-sectional areas of each of the pipes,
A1 and A2, are given by
A1 =
π
4
D2
1 =
π
4
(0.05)2
= 0.001963 m2
A2 =
π
4
D2
2 =
π
4
(0.10)2
= 0.007854 m2
When the flowrate, Q, is 5 L/s, the velocities V1 and V2 are given by
V1 =
Q
A1
=
0.005
0.001963
= 2.54 m/s
V2 =
Q
A2
=
0.005
0.007854
= 0.637 m/s
PVC pipe is considered smooth (ks ≈ 0) and therefore the friction factor, f, can be estimated using the Jain equation
f =
0.25

log10
5.74
Re0.9
2

34
where Re is the Reynolds number. At 20◦
C, the kinematic viscosity, ν, is equal to 1.00 × 10−6
m2
/s and for the
50-mm pipe
Re1 =
V1D1
ν
=
(2.51)(0.05)
1.00 × 10−6
= 1.27 × 105
which leads to
f1 =
0.25

log10
5.74
(1.27 × 105)0.9
2
= 0.0170
and for the 100-mm pipe
Re2 =
V2D2
ν
=
(0.637)(0.10)
1.00 × 10−6
= 6.37 × 104
which leads to
f2 =
0.25

log10
5.74
(6.37 × 104)0.9
2
= 0.0197
Substituting the values of these parameters into the energy equation yields
0 −

1 +
(0.0170)(8)
0.05
+ 0.25

2.542
(2)(9.81)
+ hp
−

(0.0197)(22)
0.10
+ 0.25 + 0.25 + 1

0.6372
(2)(9.81)
= 5
which leads to
hp = 6.43 m
Therefore the head to be added by the pump is 6.43 m.
Minor losses are frequently neglected in the analysis of pipeline systems. As a general rule,
neglecting minor losses is justified when, on average, there is a length of 1,000 diameters between
each minor loss (Streeter et al., 1998).
Head Losses in Noncircular Conduits. Most pipelines are of circular cross-section, but flow
of water in noncircular conduits is commonly encountered in cases such as rectangular culverts
flowing full. The hydraulic radius, R, of a conduit of any shape is defined by the relation
R =
A
P
(2.77)
where A is the cross-sectional area of the conduit and P is the wetted perimeter. For circular
conduits of diameter D, the hydraulic radius is given by
R =
πD2/4
πD
=
D
4
(2.78)
or
D = 4R (2.79)
Using the hydraulic radius, R, as the length scale of a closed conduit instead of D, the frictional
head losses, hf , in noncircular conduits can be estimated using the Darcy-Weisbach equation for
circular conduits by simply replacing D by 4R, which yields
hf =
fL
4R
V 2
2g
(2.80)

where the friction factor, f, is calculated using a Reynolds number, Re, defined by
Re =
ρV (4R)
µ
(2.81)
and a relative roughness defined by ks/4R.
Characterizing a noncircular conduit by the hydraulic radius, R, is necessarily approximate
since conduits of arbitrary cross-section cannot be described with a single parameter. Secondary
currents that are generated across a noncircular conduit cross-section to redistribute the shears
are another reason why noncircular conduits cannot be completely characterized by the hydraulic
radius (Liggett, 1994). However, according to Munson and colleagues (1994) and White (1994),
using the hydraulic radius as a basis for calculating frictional head losses in noncircular conduits
is usually accurate to within 15% for turbulent flow. This approximation is much less accurate for
laminar flows, where the accuracy is on the order of ±40% (White, 1994). Olson and Wright (1990)
state that this approach can be used for rectangular conduits where the ratio of sides, called the
aspect ratio, does not exceed about 8. Potter and Wiggert (2001) state that aspect ratios must be
less than 4:1.
Example 2.7.
Water flows through a rectangular concrete culvert of width 2 m and depth 1 m. If the length of the culvert is 10 m
and the flowrate is 6 m3
/s, estimate the head loss through the culvert. Assume that the culvert flows full.
Solution.
The head loss can be calculated using Equation 2.80. The hydraulic radius, R, is given by
R =
A
P
=
(2)(1)
2(2 + 1)
= 0.333 m
and the mean velocity, V , is given by
V =
Q
A
=
6
(2)(1)
= 3 m/s
At 20◦
C, ν = 1.00 × 10−6
m2
/s, and therefore the Reynolds number, Re, is given by
Re =
V (4R)
ν
=
(3)(4 × 0.333)
1.00 × 10−6
= 4.00 × 106
A median equivalent sand roughness for concrete can be taken as ks = 1.6 mm (Table 2.1), and therefore the relative
roughness, ks/4R, is given by
ks
4R
=
1.6 × 10−3
4(0.333)
= 0.00120
Substituting Re and ks/4R into the Jain equation (Equation 2.38) for the friction factor yields
1
√
f
= −2 log

ks/4R
3.7
+
5.74
Re0.9

= −2 log

0.00120
3.7
+
5.74
(4.00 × 106)0.9

= 6.96
which yields
f = 0.0206
The frictional head loss in the culvert, hf , is therefore given by the Darcy-Weisbach equation as
hf =
fL
4R
V 2
2g
=
(0.0206)(10)
(4 × 0.333)
32
2(9.81)
= 0.0709 m
The head loss in the culvert can therefore be estimated as 7.1 cm.

36
Empirical Friction-Loss Formulae. Friction losses in pipelines should generally be calculated
using the Darcy-Weisbach equation. However, a minor inconvenience in using the Darcy-Weisbach
equation to relate the friction loss to the flow velocity results from the dependence of the friction
factor on the flow velocity; therefore, the Darcy-Weisbach equation must be solved simultaneously
with the Colebrook equation. In modern engineering practice, computer hardware and software
make this a very minor inconvenience. In earlier years, however, this was considered a real problem,
and various empirical head-loss formulae were developed to relate the head loss directly to the flow
velocity. The most commonly used empirical formulae are the Hazen-Williams formula and the
Manning formula.
The Hazen-Williams formula (Williams and Hazen, 1920) is applicable only to the flow of water
in pipes and is given by
V = 0.849CHR0.63
S0.54
f (2.82)
where V is the flow velocity (in m/s), CH is the Hazen-Williams roughness coefficient, R is the
hydraulic radius (in m), and Sf is the slope of the energy grade line, defined by
Sf =
hf
L
(2.83)
where hf is the head loss due to friction over a length L of pipe. Values of CH for a variety of
commonly used pipe materials are given in Table 2.2. Solving Equations 2.82 and 2.83 yields the
Table 2.2: Pipe Roughness Coefficients
CH n
Pipe material Range Typical Range Typical
Ductile and cast iron:
New, unlined 120–140 130 — 0.013
Old, unlined 40–100 80 — 0.025
Cement lined and seal coated 100–140 120 0.011–0.015 0.013
Steel:
Welded and seamless 80–150 120 — 0.012
Riveted — 110 0.012–0.018 0.015
Mortar lining 120 – 145 130 — —
Asbestos cement 140 — 0.011
Concrete 100–140 120 0.011–0.015 0.012
Vitrified clay pipe (VCP) — 110 0.012–0.014 —
Polyvinyl chloride (PVC) 135 – 150 140 0.007–0.011 0.009
Corrugated metal pipe (CMP) — — — 0.025
Source: Velon and Johnson (1993); Wurbs and James (2002).
following expression for the frictional head loss,
hf = 6.82
L
D1.17

V
CH
1.85
(2.84)
where D is the diameter of the pipe. The Hazen-Williams equation is applicable to the flow of
water at 16◦C in pipes with diameters between 50 mm and 1850 mm, and flow velocities less

than 3 m/s (Mott, 1994). Outside of these conditions, use of the Hazen-Williams equation is
strongly discouraged. To further support these quantitative limitations, Street and colleagues
(1996) and Liou (1998) have shown that the Hazen-Williams coefficient has a strong Reynolds
number dependence, and is mostly applicable where the pipe is relatively smooth and in the early
part of its transition to rough flow. Furthermore, Jain and colleagues (1978) have shown that an
error of up to 39% can be expected in the evaluation of the velocity by the Hazen-Williams formula
over a wide range of diameters and slopes. In spite of these cautionary notes, the Hazen-Williams
formula is frequently used in the United States for the design of large water-supply pipes without
regard to its limited range of applicability, a practice that can have very detrimental effects on pipe
design and could potentially lead to litigation (Bombardelli and Garcı́a, 2003).
A second empirical formula that is sometimes used to describe flow in pipes is the Manning
formula, which is given by
V =
1
n
R
2
3 S
1
2
f (2.85)
where V , R, and Sf have the same meaning and units as in the Hazen-Williams formula, and n is
the Manning roughness coefficient. Values of n for a variety of commonly used pipe materials are
given in Table 2.2 (Velon and Johnson, 1993). Solving Equations 2.85 and 2.83 yields the following
expression for the frictional head loss
hf = 6.35
n2LV 2
D
4
3
(2.86)
The Manning formula applies to fully turbulent flows, where the frictional head losses depend pri-
marily on the relative roughness.
Example 2.8.
Water flows at a velocity of 1 m/s in a 150 mm new ductile iron pipe. Estimate the head loss over 500 m using: (a)
the Hazen-Williams formula, (b) the Manning formula, and (c) the Darcy-Weisbach equation. Compare your results.
Solution.
(a) The Hazen-Williams roughness coefficient, CH , can be taken as 130 (Table 2.2), L = 500 m, D = 0.150 m,
V = 1 m/s, and therefore the head loss, hf , is given by Equation 2.84 as
hf = 6.82
L
D1.17

V
CH
1.85
= 6.82
500
(0.15)1.17

1
130
1.85
= 3.85 m
(b) The Manning roughness coefficient, n, can be taken as 0.013 (approximation from Table 2.2), and therefore
the head loss, hf , is given by Equation 2.86 as
hf = 6.35
n2
LV 2
D
4
3
= 6.35
(0.013)2
(500)(1)2
(0.15)
4
3
= 6.73 m
(c) The equivalent sand roughness, ks, can be taken as 0.26 mm (Table 2.1), and the Reynolds number, Re, is
given by
Re =
V D
ν
=
(1)(0.15)
1.00 × 10−6
= 1.5 × 105
where ν = 1.00 × 10−6
m2
/s at 20◦
C. Substituting ks, D, and Re into the Colebrook equation yields the
friction factor, f, where
1
√
f
= −2 log

ks
3.7D
+
2.51
Re
√
f

= −2 log

0.26
3.7(150)
+
2.51
1.5 × 105
√
f

38
Solving by trial and error leads to
f = 0.0238
The head loss, hf , is therefore given by the Darcy-Weisbach equation as
hf = f
L
D
V 2
2g
= 0.0238
500
0.15
12
2(9.81)
= 4.04 m
It is reasonable to assume that the Darcy-Weisbach equation yields the most accurate estimate of the head loss.
In this case, the Hazen-Williams formula gives a head loss that is 5% too low and the Manning formula yields a head
loss that is 67% too high.
2.3 Pipe Networks
Pipe networks are commonly encountered in the context of water-distribution systems. The perfor-
mance criteria of these systems are typically specified in terms of minimum flow rates and pressure
heads that must be maintained at the specified points in the network. Analyses of pipe networks
are usually within the context of (1) designing a new network, (2) designing a modification to an
existing network, and/or (3) evaluating the reliability of a network. The procedure for analyzing
a pipe network usually aims at finding the flow distribution within the network, with the pressure
distribution being derived from the flow distribution using the energy equation. A typical pipe
network is illustrated in Figure 2.9, where the boundary conditions consist of inflows, outflows, and
constant-head boundaries such as storage reservoirs. Inflows are typically from water-treatment fa-
A B
D
Loop
Node
(a)
C
Q3 Q1
Q2
Q5
Qa1
Qb1
B
A
C
D
(b)
Q5
Qd1
Qd2
Qc1
Qc2
Qa2
Qb2
Figure 2.9: Typical Pipe Network
cilities, outflows from consumer withdrawals or fires. All outflows are assumed to occur at network
junctions.
The basic equations to be satisfied in pipe networks are the continuity and energy equations.
The continuity equation requires that, at each node in the network, the sum of the outflows is equal
to the sum of the inflows. This requirement is expressed by the relation
NP(j)

i=1
Qij − Fj = 0, j = 1, NJ (2.87)

where Qij is the flowrate in pipe i at junction j (inflows positive); NP(j) is the number of pipes
meeting at junction j; Fj is the external flow rate (outflows positive) at junction j; and NJ is the
total number of junctions in the network. The energy equation requires that the heads at each
of the nodes in the pipe network be consistent with the head losses in the pipelines connecting
the nodes. There are two principal methods of calculating the flows in pipe networks: the nodal
method and the loop method. In the nodal method, the energy equation is expressed in terms of
the heads at the network nodes, while in the loop method the energy equation is expressed in terms
of the flows in closed loops within the pipe network.
2.3.1 Nodal Method
In the nodal method, the energy equation is written for each pipeline in the network as
h2 = h1 −

fL
D
+

km

Q|Q|
2gA2
+
Q
|Q|
hp (2.88)
where h2 and h1 are the heads at the upstream and downstream ends of a pipe; the terms in
parentheses measure the friction loss and minor losses, respectively; and hp is the head added
by pumps in the pipeline. The energy equation stated in Equation 2.88 has been modified to
account for the fact that the flow direction is in many cases unknown, in which case a positive
flow direction in each pipeline must be assumed, and a consistent set of energy equations stated
for the entire network. Equation 2.88 assumes that the positive flow direction is from node 1 to
node 2. Application of the nodal method in practice is usually limited to relatively simple networks.
Example 2.9.
The high-pressure ductile-iron pipeline shown in Figure 2.10 becomes divided at point B and rejoins at point C. The
pipeline characteristics are given in the following tables.
Flow
A B
3
2
1
C D
4
pD 5 ?
pA 5 900 kPa
Figure 2.10: Pipe Network

40
Diameter Length
Pipe (mm) (m)
1 750 500
2 400 600
3 500 650
4 700 400
Elevation
Location (m)
A 5.0
B 4.5
C 4.0
D 3.5
If the flowrate in Pipe 1 is 2 m3
/s and the pressure at point A is 900 kPa, calculate the pressure at point D. Assume
that the flows are fully turbulent in all pipes.
Solution.
The equivalent sand roughness, ks, of ductile-iron pipe is 0.26 mm, and the pipe and flow characteristics are as
follows:
Area Velocity
Pipe (m2
) (m/s) ks/D f
1 0.442 4.53 0.000347 0.0154
2 0.126 — 0.000650 0.0177
3 0.196 — 0.000520 0.0168
4 0.385 5.20 0.000371 0.0156
where it has been assumed that the flows are fully turbulent. Taking γ = 9.79 kN/m3
, the head at location A, hA,
is given by
hA =
pA
γ
+
V 2
1
2g
+ zA =
900
9.79
+
4.532
(2)(9.81)
+ 5 = 98.0 m
and the energy equations for each pipe are as follows
Pipe 1: hB = hA −
f1L1
D1
V 2
1
2g
= 98.0 −
(0.0154)(500)
0.75
4.532
(2)(9.81)
= 87.3 m (2.89)
Pipe 2: hC = hB −
f2L2
D2
Q2
2
2gA2
2
= 87.3 −
(0.0177)(600)
0.40
Q2
2
(2)(9.81)(0.126)2
= 87.3 − 85.2Q2
2 (2.90)
Pipe 3: hC = hB −
f3L3
D3
Q2
3
2gA2
3
= 87.3 −
(0.0168)(650)
0.50
Q2
3
(2)(9.81)(0.196)2
= 87.3 − 29.0Q2
3 (2.91)
Pipe 4: hD = hC −
f4L4
D4
Q2
4
2gA2
4
= hC −
(0.0156)(400)
0.70
Q2
4
(2)(9.81)(0.385)2
= hC − 3.07Q2
4 (2.92)
and the continuity equations at the two pipe junctions are
Junction B: Q2 + Q3 = 2 m3
/s (2.93)
Junction C: Q2 + Q3 = Q4 (2.94)
Equations 2.90 to 2.94 are five equations in five unknowns: hC , hD, Q2, Q3, and Q4. Equations 2.93 and 2.94 indicate
that
Q4 = 2 m3
/s

Combining Equations 2.90 and 2.91 leads to
87.3 − 85.2Q2
2 = 87.3 − 29.0Q2
3
and therefore
Q2 = 0.583Q3 (2.95)
Substituting Equation 2.95 into Equation 2.93 yields
2 = (0.583 + 1)Q3
or
Q3 = 1.26 m3
/s
and from Equation 2.95
Q2 = 0.74 m3
/s
According to Equation 2.91
hC = 87.3 − 29.0Q2
3 = 87.3 − 29.0(1.26)2
= 41.3 m
and Equation 2.92 gives
hD = hC − 3.07Q2
4 = 41.3 − 3.07(2)2
= 29.0 m
Therefore, since the total head at D, hD, is equal to 29.0 m, then
29.0 =
pD
γ
+
V 2
4
2g
+ zD =
pD
9.79
+
5.202
(2)(9.81)
+ 3.5
which yields
pD = 236 kPa
Therefore, the pressure at location D is 236 kPa.
This problem has been solved by assuming that the flows in all pipes are fully turbulent. This is generally not
known for sure a priori, and therefore a complete solution would require repeating the calculations until the assumed
friction factors are consistent with the calculated flowrates.
2.3.2 Loop Method
In the loop method, the energy equation is written for each loop of the network, in which case the
algebraic sum of the head losses within each loop is equal to zero. This requirement is expressed
by the relation
NP(i)

j=1
(hL,ij − hp,ij) = 0, i = 1, NL (2.96)
where hL,ij is the head loss in pipe j of loop i, and hp,ij is the head added by any pumps that may
exist in line ij. Combining Equations 2.87 and 2.96 with an expression for calculating the head losses
in pipes, such as the Darcy-Weisbach equation, and the pump characteristic curves, which relate
the head added by the pump to the flowrate through the pump, yields a complete mathematical
description of the flow problem. Solution of this system of flow equations is complicated by the
fact that the equations are nonlinear, and numerical methods must be used to solve for the flow
distribution in the pipe network.

42
Hardy Cross Method. The Hardy Cross method (Cross, 1936) is a simple technique for hand-
solution of the loop system of equations governing flow in pipe networks. This iterative method
was developed before the advent of computers, and much more efficient algorithms are used for
numerical computations. In spite of this limitation, the Hardy Cross method is presented here to
illustrate the iterative solution of the loop equations in pipe networks. The Hardy Cross method
assumes that the head loss, hL, in each pipe is proportional to the discharge, Q, raised to some
power n, in which case
hL = rQn
(2.97)
The proportionality constant, r, depends on which head loss equation is used and the types of
losses in the pipe. Clearly, if all head losses are due to friction and the Darcy-Weisbach equation
is used to calculate the head losses, then r is given by
r =
fL
2gA2D
(2.98)
If the flow in each pipe is approximated as Q̂, and ∆Q is the error in this estimate, then the actual
flowrate, Q, is related to Q̂ and ∆Q by
Q = Q̂ + ∆Q (2.99)
and the head loss in each pipe is given by
hL = rQn
= r(Q̂ + ∆Q)n
= r

Q̂n
+ nQ̂n−1
∆Q +
n(n − 1)
2
Q̂n−2
(∆Q)2
+ · · · + (∆Q)n

(2.100)
If the error in the flow estimate, ∆Q, is small, then the higher order terms in ∆Q can be neglected
and the head loss in each pipe can be approximated by the relation
hL ≈ rQ̂n
+ rnQ̂n−1
∆Q (2.101)
This relation approximates the head loss in the flow direction. However, in working with pipe
networks, it is required that the algebraic sum of the head losses in any loop of the network (see
Figure 2.9) must be equal to zero. We must therefore define a positive flow direction (such as
clockwise), and count head losses as positive in pipes when the flow is in the positive direction and
negative when the flow is opposite to the selected positive direction. Under these circumstances,
the sign of the head loss must be the same as the sign of the flow direction. Further, when the
flow is in the positive direction, positive values of ∆Q require a positive correction to the head loss;
when the flow is in the negative direction, positive values in ∆Q also require a positive correction
to the calculated head loss. To preserve the algebraic relation among head loss, flow direction, and
flow error (∆Q), Equation 2.101 for each pipe can be written as
hL = rQ̂|Q̂|n−1
+ rn|Q̂|n−1
∆Q (2.102)
where the approximation has been replaced by an equal sign. On the basis of Equation 2.102, the
requirement that the algebraic sum of the head losses around each loop be equal to zero can be
written as
NP(i)

j=1
rijQj|Qj|n−1
+ ∆Qi
NP(i)

j=1
rijn|Qj|n−1
= 0, i = 1, NL (2.103)

where NP(i) is the number of pipes in loop i, rij is the head-loss coefficient in pipe j (in loop i),
Qj is the estimated flow in pipe j, ∆Qi is the flow correction for the pipes in loop i, and NL is
the number of loops in the entire network. The approximation given by Equation 2.103 assumes
that there are no pumps in the loop, and that the flow correction, ∆Qi, is the same for each pipe
in each loop. Solving Equation 2.103 for ∆Qi leads to
∆Qi = −
NP(i)
j=1 rijQj|Qj|n−1
NP(i)
j=1 nrij|Qj|n−1
(2.104)
This equation forms the basis of the Hardy Cross method.
The steps to be followed in using the Hardy Cross method to calculate the flow distribution in
pipe networks are:
1. Assume a reasonable distribution of flows in the pipe network. This assumed flow distribution
must satisfy continuity.
2. For each loop, i, in the network, calculate the quantities rijQj|Qj|n−1 and nrij|Qj|n−1 for
each pipe in the loop. Calculate the flow correction, ∆Qi, using Equation 2.104. Add the
correction algebraically to the estimated flow in each pipe. [Note: Values of rij occur in
both the numerator and denominator of Equation 2.104; therefore, values proportional to the
actual rij may be used to calculate ∆Qi.]
3. Proceed to another circuit and repeat step 2.
4. Repeat steps 2 and 3 until the corrections (∆Qi) are small.
The application of the Hardy Cross method is best demonstrated by an example.
Example 2.10.
Compute the distribution of flows in the pipe network shown in Figure 2.11(a), where the head loss in each pipe is
given by
hL = rQ2
and the values of r are shown in Figure 2.11(a). The flows are taken as dimensionless for the sake of illustration.
(a)
20
100
50
30
r 5 1
r 5 5
r 5 3
r 5 2
r 5 6
(b)
20
100
50
30
15
1 2
4 3
30
35
II
35
70
I
Figure 2.11: Flows in Pipe Network
Solution.
The first step is to assume a distribution of flows in the pipe network that satisfies continuity. The assumed distribution

44
of flows is shown in Figure 2.11(b), along with the positive-flow directions in each of the two loops. The flow correction
for each loop is calculated using Equation 2.104. Since n = 2 in this case, the flow correction formula becomes
∆Qi = −
NP (i)
j=1
rijQj|Qj|
NP (i)
j=1
2rij|Qj|
The calculation of the numerator and denominator of this flow correction formula for loop I is tabulated as follows
Loop Pipe Q rQ|Q| 2r|Q|
I 4–1 70 29,400 840
1–3 35 3,675 210
3–4 −30 −4,500 300
28,575 1,350
The flow correction for loop I, ∆QI , is therefore given by
∆QI = −
28575
1350
= −21.2
and the corrected flows are
Loop Pipe Q
I 4–1 48.8
1–3 13.8
3–4 −51.2
Moving to loop II, the calculation of the numerator and denominator of the flow correction formula for loop II is
given by
Loop Pipe Q rQ|Q| 2r|Q|
II 1–2 15 225 30
2–3 −35 −2,450 140
3–1 −13.8 −574 83
−2,799 253
The flow correction for loop II, ∆QII , is therefore given by
∆QII = −
−2799
253
= 11.1
and the corrected flows are
Loop Pipe Q
II 1–2 26.1
2–3 −23.9
3–1 −2.7
This procedure is repeated in the following table until the calculated flow corrections do not affect the calculated

flows, to the level of significant digits retained in the calculations.
Iteration Loop Pipe Q rQ|Q| 2r|Q| ∆Q Corrected Q
2 I 4–1 48.8 14,289 586 47.7
1–3 2.7 22 16 1.6
3–4 −51.2 −13,107 512 −52.3
1,204 1,114 −1.1
II 1–2 26.1 681 52 29.1
2–3 −23.9 −1,142 96 −20.9
3–1 −1.6 −8 10 1.4
−469 157 3.0
3 I 4–1 47.7 13,663 573 47.7
1–3 1.4 6 8 1.4
3–4 −52.3 −13,666 523 −52.3
3 1,104 0.0
II 1–2 29.1 847 58 29.2
2–3 −20.9 −874 84 −20.8
3–1 1.4 6 8 1.5
−21 150 0.1
4 I 4–1 47.7 13,662 573 47.7
1–3 1.5 7 9 1.5
3–4 −52.3 −13,668 523 −52.3
1 1,104 0.0
II 1–2 29.2 853 58 29.2
2–3 −20.8 −865 83 −20.8
3–1 1.5 7 9 1.5
−5 150 0.0
The final flow distribution, after four iterations, is given by
Pipe Q
1–2 29.2
2–3 −20.8
3–4 −52.3
4–1 47.7
1–3 −1.5
It is clear that the final results are fairly close to the flow estimates after only one iteration.
As the above example illustrates, complex pipe networks can generally be treated as a combi-
nation of simple circuits or loops, with each balanced in turn until compatible flow conditions exist
in all loops. Typically, after the flows have been computed for all pipes in a network, the elevation
of the hydraulic grade line and the pressure are computed for each junction node. These pressures
are then assessed relative to acceptable operating pressures.
In practice, analyses of complex pipe networks are usually done using commercial computer
programs that solve the system of continuity and energy equations that govern the flows in pipe

46
networks. These computer programs, such as EPANET (Rossman, 2000), generally use algorithms
that are computationally more efficient than the Hardy Cross method, such as the linear theory
method, the Newton-Raphson method, and the gradient algorithm (Lansey and Mays, 1999).
2.4 Pumps
Pumps are hydraulic machines that convert mechanical energy to fluid energy. They can be clas-
sified into two main categories: (1) positive displacement pumps, and (2) rotodynamic or kinetic
pumps. Positive displacement pumps deliver a fixed quantity of fluid with each revolution of the
pump rotor, such as with a piston or cylinder, while rotodynamic pumps add energy to the fluid
by accelerating it through the action of a rotating impeller. Rotodynamic pumps are far more
common in engineering practice and will be the focus of this section.
Three types of rotodynamic pumps commonly encountered are centrifugal pumps, axial-flow
pumps, and mixed-flow pumps. In centrifugal pumps, the flow enters the pump chamber along
the axis of the impeller and is discharged radially by centrifugal action, as illustrated in Figure
2.12(a). In axial-flow pumps, the flow enters and leaves the pump chamber along the axis of the
Flow
Flow
Input
shaft
Inlet
vane
Outlet
vane
Impeller
(b) Axial flow pump
(a) Centrifugal pump
A View A–A
A
Flow
v
Casing
Eye of
impeller
Impeller
Eye of
impeller
Figure 2.12: Types of Pumps

impeller, as shown in Figure 2.12(b). In mixed-flow pumps, outflows have both radial and axial
components. Typical centrifugal and axial-flow pump installations are illustrated in Figure 2.13.
Key components of the centrifugal pump are a foot valve installed in the suction pipe to prevent
Centrifugal
pump
(a)
(b)
Strainer
Foot valve
Gate valve
Check valve
Shaft
Propeller blade
Guide vane
Motor
Figure 2.13: Centrifugal and Axial Flow Pump Installations
Source: Finnemore and Franzini (2002).
water from leaving the pump when it is stopped and a check valve in the discharge pipe to prevent
backflow if there is a power failure. If the suction line is empty prior to starting the pump, then
the suction line must be primed prior to startup. Unless the water is known to be very clean, a
strainer should be installed at the inlet to the suction piping. The pipe size of the suction line
should never be smaller than the inlet connection on the pump; if a reducer is required, it should
be of the eccentric type since concentric reducers place part of the supply pipe above the pump
inlet where an air pocket could form. The discharge line from the pump should contain a valve
close to the pump to allow service or pump replacement.
The pumps illustrated in Figure 2.13 are both single-stage pumps, which means that they have
only one impeller. In multistage pumps, two or more impellers are arranged in series in such a
way that the discharge from one impeller enters the eye of the next impeller. If a pump has three

48
impellers in series, it is called a three-stage pump. Multistage pumps are typically used when large
pumping heads are required.
The performance of a pump is measured by the head added by the pump and the pump efficiency.
The head added by the pump, hp, is equal to the difference between the total head on the discharge
side of the pump and the total head on the suction side of the pump, and is sometimes referred to
as the total dynamic head. The efficiency of the pump, η, is defined by
η =
power delivered to the fluid
power supplied to the shaft
(2.105)
Pumps are inefficient for a variety of reasons, such as frictional losses as the fluid moves over the solid
surfaces, separation losses, leakage of fluid between the impeller and the casing, and mechanical
losses in the bearings and sealing glands of the pump. The pump-performance parameters, hp and
η, can be expressed in terms of the fluid properties and the physical characteristics of the pump by
the functional relation
ghp or η = f1(ρ, µ, D, ω, Q) (2.106)
where the energy added per unit mass of fluid, ghp, is used instead of hp (to remove the effect of
gravity), f1 is an unknown function, ρ and µ are the density and dynamic viscosity of the fluid
respectively, Q is the flowrate through the pump, D is a characteristic dimension of the pump
(usually the inlet or outlet diameter), and ω is the speed of the pump impeller. Equation 2.106 is
a functional relationship between six variables in three dimensions. According to the Buckingham
pi theorem, this relationship can be expressed as a relation between three dimensionless groups as
follows
ghp
ω2D2
or η = f2

Q
ωD3
,
ρωD2
µ

(2.107)
where ghp/ω2D2 is called the head coefficient, and Q/ωD3 is called the flow coefficient (Douglas
et al., 1995). In most cases, the flow through the pump is fully turbulent and viscous forces are
negligible relative to the inertial forces. Under these circumstances, the viscosity of the fluid is
neglected and Equation 2.107 becomes
ghp
ω2D2
or η = f3

Q
ωD3

(2.108)
This relationship describes the performance of all pumps in which viscous effects are negligible, but
the exact form of the function in Equation 2.108 depends on the geometry of the pump. A series
of pumps having the same shape (but different sizes) are expected to have the same functional
relationships between ghp/(ω2D2) and Q/(ωD3) as well as η and Q/(ωD3). A class of pumps
that have the same shape is called a homologous series, and the performance characteristics of
a homologous series of pumps are described by curves such as those in Figure 2.14. Pumps are
selected to meet specific design conditions and, since the efficiency of a pump varies with the
operating condition, it is usually desirable to select a pump that operates at or near the point of
maximum efficiency, indicated by the point P in Figure 2.14.
The point of maximum efficiency of a pump is commonly called the best efficiency point (bep),
and is sometimes called the nameplate or design point. Maintaining operation near the bep will
allow a pump to function for years with little maintenance, and as the operating point moves
away from the bep, pump thrust and radial loads increase which increases the wear on the pump

Efficiency
curve
hmax
h
K1
K2
P
v2
D2
ghp
vD3
Q
Figure 2.14: Performance Curves of a Homologous Series of Pumps
bearings and shaft. For these reasons, it is generally recommended that pump operation should be
maintained between 70% and 130% of the bep flowrate (Lansey and El-Shorbagy, 2001). At the
best efficiency point in Figure 2.14,
ghp
ω2D2
= K1, and
Q
ωD3
= K2 (2.109)
Eliminating D from these equations yields
ωQ
1
2
(ghp)
3
4
=

K2
K
3
2
1
(2.110)
The term on the righthand side of this equation is a constant for a homologous series of pumps and
is denoted by the specific speed, ns, defined by
ns =
ωQ
1
2
(ghp)
3
4
(2.111)
where any consistent set of units can be used. The specific speed, ns, is also called the shape
number (Hwang and Houghtalen, 1996; Wurbs and James, 2002) or the type number (Douglas et
al., 2001). In SI units, ω is in rad/s, Q in m3/s, g in m/s2, and hp in meters. The most efficient
operating point for a homologous series of pumps is therefore specified by the specific speed. This
nomenclature is somewhat unfortunate since the specific speed is dimensionless and hence does not
have units of speed. It is common practice in the United States to define the specific speed by Ns,
as
Ns =
ωQ
1
2
h
3
4
p
(2.112)
where Ns is not dimensionless, ω is in revolutions per minute (rpm), Q is in gallons per minute
(gpm), and hp is in feet (ft). Although Ns has dimensions, the units are seldom stated in practice.
The required pump operating point gives the flowrate, Q, and head, hp, required from the pump;
the rotational speed, ω, is determined by the synchronous speeds of available motors; and the
specific speed calculated from the required operating point is the basis for selecting the appropriate
pump. Since the specific speed is independent of the size of a pump, and all homologous pumps
(of varying sizes) have the same specific speed, then the calculated specific speed at the desired
operating point indicates the type of pump that must be selected to ensure optimal efficiency.

50
Table 2.3: Pump Selection Guidelines
Typical Typical
Range of flowrates efficiencies
Type of pump specific speeds, ns
∗ (L/s) (%)
Centrifugal 0.15–1.5 (400–4,000) 60 70–94
Mixed flow 1.5–3.7 (4,000–10,000) 60–300 90–94
Axial flow 3.7–5.5 (10,000–15,000) 300 84–90
∗
The specific speeds in parentheses correspond to Ns given by Equation 2.112, with ω in rpm, Q in gpm, and hp in
ft.
The types of pump that give the maximum efficiency for given specific speeds, ns, are listed in
Table 2.3 along with typical flowrates delivered by the pumps. Table 2.3 indicates that centrifugal
pumps have low specific speeds, ns 1.5; mixed-flow pumps have medium specific speeds, 1.5
ns 3.7; and axial-flow pumps have high specific speeds, ns 3.7. This indicates that centrifugal
pumps are most efficient at delivering low flows at high heads, while axial flow pumps are most
efficient at delivering high flows at low heads. The efficiencies of radial-flow (centrifugal) pumps
increase with increasing specific speed, while the efficiencies of mixed-flow and axial-flow pumps
decrease with increasing specific speed. Pumps with specific speed less than 0.3 tend to be inefficient
(Finnemore and Franzini, 2002). Since axial-flow pumps are most efficient at delivering high flows
at low heads, this type of pump is commonly used to move large volumes of water through major
canals, and an example of this application is shown in Figure 2.15; where there are three axial-flow
pumps operating in parallel, and these pumps are driven by motors housed in the pump station.
Figure 2.15: Axial Flow Pump Operating in a Canal
Most pumps are driven by standard electric motors. The standard speed of AC synchronous
induction motors at 60 cycles and 220 to 440 volts is given by
Synchronous speed (rpm) =
3600
no. of pairs of poles
(2.113)
A common problem is that, for the motor speed chosen, the calculated specific speed does not
exactly equal the specific speed of available pumps. In these cases, it is recommended to choose a

pump with a specific speed that is close to and greater than the required specific speed. In rare
cases, a new pump may be designed to meet the design conditions exactly, however, this is usually
very costly and only justified for very large pumps.
2.4.1 Affinity Laws
The performance curves for a homologous series of pumps is illustrated in Figure 2.14. Any two
pumps in the homologous series are expected to operate at the same efficiency when

Q
ωD3

1
=

Q
ωD3

2
, and

hp
ω2D2

1
=

hp
ω2D2

2
(2.114)
These relationships are sometimes called the affinity laws for homologous pumps. An affinity law
for the power delivered to the fluid, P, can be derived from the affinity relations given in Equation
2.114, since P is defined by
P = γQhp (2.115)
which leads to the following derived affinity relation

P
ω3D5

1
=

P
ω3D5

2
(2.116)
In accordance with the dimensional analysis of pump performance, Equation 2.107, the affinity
laws for scaling pump performance are valid as long as viscous effects are negligible. The effect of
viscosity is measured by the Reynolds number, Re, defined by
Re =
ρωD2
µ
(2.117)
and scale effects are negligible when Re 3×105 (Gerhart et al., 1992). In lieu of stating a Reynolds
number criterion for scale effects to be negligible, it is sometimes stated that larger pumps are more
efficient than smaller pumps and that the scale effect on efficiency is given by (Moody and Zowski,
1969; Stepanoff, 1957)
1 − η2
1 − η1
=

D1
D2
1
4
(2.118)
where η1 and η2 are the efficiencies of homologous pumps of diameters D1 and D2, respectively.
The effect of changes in flowrate on efficiency can be estimated using the relation
0.94 − η2
0.94 − η1
=

Q1
Q2
0.32
(2.119)
where Q1 and Q2 are corresponding homologous flowrates.
Example 2.11.
A pump with a 1,200 rpm motor has a performance curve of
hp = 12 − 0.1Q2

52
where hp is in meters and Q is in cubic meters per minute. If the motor is changed to 2,400 rpm, estimate the new
performance curve.
Solution.
The performance characteristics of a homologous series of pumps is given by
ghp
ω2D2
= f

Q
ωD3

For a fixed pump size, D, for two different motor speeds, ω1 and ω2, the general performance curve can be written as
h1
ω2
1
= f

Q1
ω1

and
h2
ω2
2
= f

Q2
ω2

where h1 and Q1 are the head added by the pump and the flowrate, respectively, when the speed is ω1; and h2 and
Q2 are the head and flowrate when the speed is ω2. Since the pumps are part of a homologous series, then, neglecting
scale effects, the function f is fixed and therefore when
Q1
ω1
=
Q2
ω2
then
h1
ω2
1
=
h2
ω2
2
These relations are simply statements of the affinity laws. In the present case, ω1 = 1,200 rpm and ω2 = 2,400 rpm
and the affinity laws give that
Q1 =
ω1
ω2
Q2 =
1200
2400
Q2 = 0.5Q2
h1 =
ω2
1
ω2
2
h2 =
12002
24002
h2 = 0.25h2
Since the performance curve of the pump at speed ω1 is given by
h1 = 12 − 0.1Q2
1
then the performance curve at speed ω2 is given by
0.25h2 = 12 − 0.1(0.5Q2)2
which leads to
h2 = 48 − 0.1Q2
2
The performance curve of the pump with a 2,400 rpm motor is therefore given by
hp = 48 − 0.1Q2
2.4.2 Pump Selection
Selection of a pump generally requires specification of a manufacturer, model (homologous) series,
impeller size, D, and rotational speed, ω. For each model series and rotational speed, pump
manufacturers provide a performance curve or characteristic curve that shows the relationship
between the head, hp, added by the pump and the flowrate, Q, through the pump. A typical
example of a set of pump characteristic curves (hp versus Q) provided by a manufacturer for a

Figure 2.16: Pump Performance Curve
Source: Goulds Pumps (www.gouldspumps.com).
homologous series of pumps is shown in Figure 2.16. In this case, the homologous series of pumps
(Model 3409) have impeller diameters ranging from 12.1 in. (307 mm) to 17.5 in. (445 mm)
with a rotational speed of 885 revolutions per minute. Superimposed on the characteristic curves
are constant-efficiency lines for efficiencies ranging from 55% to 86%, and (dashed) isolines of net
positive suction head which is the allowable difference between the pressure head on the suction
side of the pump and the pressure head at which water vaporizes (i.e. saturation vapor pressure).
In Figure 2.16, the allowable net positive suction head ranges from 16 ft (4.9 m) for higher flowrates
down to approximately zero, which is indicated by a bold line that meets the 55% efficiency contour.
Also shown in Figure 2.16, below the characteristic curves, is the power delivered to the pump (in
kW) for various flowrates and impeller diameters. This power input to the pump shaft is called
the brake horsepower.
The goal in pump selection is to select a pump that operates at a point of maximum efficiency
and with a net positive suction head that exceeds the minimum allowable value. Pumps are placed
in pipeline systems such as that illustrated in Figure 2.17, in which case the energy equation for

54
the pipeline system requires that the head, hp, added by the pump is given by
hp = ∆z + Q2

fL
2gA2D
+
Km
2gA2

(2.120)
where ∆z is the difference in elevation between the water surfaces of the inflow and outflow reser-
voirs, the first term in the square brackets is the sum of the head losses due to friction, and the
second term is the sum of the minor head losses. Equation 2.120 gives a relationship between hp
P
Pump
Dz
Q
Q
Figure 2.17: Pipeline System
and Q for the pipeline system, and this relationship is commonly called the system curve. Because
the flowrate and head added by the pump must satisfy both the system curve and the pump charac-
teristic curve, Q and hp are determined by simultaneous solution of Equation 2.120 and the pump
characteristic curve. The resulting values of Q and hp identify the operating point of the pump.
The location of the operating point on the performance curve is illustrated in Figure 2.18.
0
System curve
Pump
characteristic
curve
Operating
point
Pump
head,
h
p
Flowrate, Q
Dz
Figure 2.18: Operating Point in Pipeline System
Example 2.12.
Water is being pumped from a lower to an upper reservoir through a pipeline system similar to the one shown in
Figure 2.17. The reservoirs differ in elevation by 15.2 m, and the length of the steel pipe (ks = 0.046 mm) connecting
the reservoirs is 21.3 m. The pipeline is 50-mm in diameter, and the performance curve of the 2400-rpm centrifugal
pump being considered for selection is given by
hp = 24.4 − 7.65Q2
(2.121)

where hp is in meters and Q is in liters per second. Using this pump, what flow do you expect in the pipeline? If the
calculated operating point of the pump coincides with the point of maximum efficiency, which is the goal of pump
selection, calculate the specific speed of the pump in U.S. Customary units and verify that a centrifugal-type pump
should be used.
Solution.
Neglecting minor losses, the energy equation for the pipeline system is given by
hp = 15.2 +
fL
2gA2D
Q2
(2.122)
where hp is the head added by the pump, f is the friction factor, L is the pipe length, A is the cross-sectional area
of the pipe, and D is the diameter of the pipe. The area, A, is given by
A =
π
4
D2
=
π
4
(0.05)2
= 0.00196 m2
In general, f is a function of both the Reynolds number and the relative roughness. However, if the flow is fully
turbulent, then the friction factor depends only on the relative roughness according to Equation 2.34
1
√
f
= −2 log

3.7

(2.123)
where is the relative roughness of the pipe given by
=
ks
D
and ks is the equivalent sand roughness. In this case, ks = 0.046 mm and D = 50 mm. Therefore
=
0.046
50
= 0.000920
Substituting for into Equation 2.123 yields
1
√
f
= −2 log

0.000920
3.7

= 7.21
Therefore
f = 0.0192
Substituting this value of f into the system equation (Equation 2.122) yields
hp = 15.2 +
fL
2gA2D
Q2
= 15.2 +
(0.0192)(21.3)
(2)(9.81)(0.00196)2(0.05)
Q2
= 15.2 + 108500Q2
This equation is for Q in m3
/s, and the corresponding equation for Q in L/s is
hp = 15.2 + 0.109Q2
(2.124)
Combining the system curve, Equation 2.124, with the pump characteristic curve, Equation 2.121, leads to
15.2 + 0.109Q2
= 24.4 − 7.65Q2
Q = 1.09 L/s
This flowrate was derived by assuming that the flow in the pipeline is fully turbulent. This assumption can now be
verified by recalculating the friction factor with the Reynolds number corresponding to the calculated flowrate. The
velocity in the pipeline, V , is given by
V =
Q
A
=
1.09 × 10−3
0.00196
= 0.556 m/s
Since the kinematic viscosity, ν, at 20◦
C is 1.00 × 10−6
m2
/s, the Reynolds number, Re, is
Re =
V D
ν
=
(0.556)(0.05)
1.00 × 10−6
= 2.78 × 104

56
The friction factor can now be recalculated using the Jain equation (Equation 2.38), where
1
√
f
= −2 log

3.7
+
5.74
Re0.9

= −2 log

0.000920
3.7
+
5.74
(2.78 × 104)0.9

= 6.17
which leads to
f = 0.0263
Therefore, the original approximation of f = 0.0192 was in error and the estimation of the flow in the pipeline must
be recalculated using f = 0.0263. After calculating the revised flow, the friction factor must again be calculated to
see if it is equal to the assumed value. If not, the process is repeated until the assumed and calculated friction factors
are equal. In this case, one more iteration shows that f = 0.0263 and
Q = 1.09 L/s
According to the pump characteristic curve, the head added by the pump, hp, is
hp = 24.4 − 7.65Q2
= 24.4 − 7.65(1.09)2
= 15.3 m
In U.S. Customary units, Q = 1.09 L/s = 17.3 gpm; hp = 15.3 m = 50.2 ft; ω = 2,400 rpm; and the specific speed,
Ns, is given by Equation 2.112 as
Ns =
ωQ
1
2
h
3
4
p
=
(2400)(17.3)
1
2
(50.2)
3
4
= 529
According to Table 2.3, with a pump operating at a specific speed of Ns = 529, the best type of pump is a centrifugal
pump.
2.4.3 Limits on Pump Location
If the absolute pressure on the suction side of a pump falls below the saturation vapor pressure
of the fluid, the water will begin to vaporize. This process of vaporization is called cavitation.
Cavitation is usually a transient phenomenon that occurs as water enters the low-pressure suction
side of a pump and experiences the even lower pressures adjacent to the rotating pump impeller. As
the water containing vapor cavities moves toward the high-pressure environment of the discharge
side of the pump, the vapor cavities are compressed and ultimately implode, creating small localized
high-velocity jets that can cause considerable damage to the pump machinery. Collapsing vapor
cavities have been associated with jet velocities on the order of 110 m/s, and pressures of up to
800 MPa when the jets strike a solid wall (Finnemore and Franzini, 2002; Knapp et al., 1970). The
damage caused by collapsing vapor cavities usually manifests itself as pitting of the metal casing
and impeller, reduced pump efficiency, and excessive vibration of the pump. The noise generated by
imploding vapor cavities resembles the sound of gravel going through a centrifugal pump. Since the
saturation vapor pressure increases with temperature, a system that operates satisfactorily without
cavitation during the winter may have problems with cavitation during the summer.
The potential for cavitation is measured by the net positive suction head, NPSH, defined as the
difference between the head on the suction side of the pump and the head when cavitation begins,
hence
NPSH =

ps
γ
+
V 2
s
2g
+ zs

−

pv
γ
+ zs

=
ps
γ
+
V 2
s
2g
−
pv
γ
(2.125)
where ps, Vs, and zs are the pressure, velocity, and elevation of the fluid at the suction side of the
pump, and pv is the saturation vapor pressure of water at the temperature of the fluid. In cases

where water is being pumped from a reservoir, the NPSH can be calculated by applying the energy
equation between the reservoir and the suction side of the pump and, in this case the calculated
NPSH is called the available net positive suction head, NPSHA, and is given by
NPSHA =
po
γ
− ∆zs − hL −
pv
γ
(2.126)
where po is the pressure at the surface of the reservoir (usually atmospheric), ∆zs is the difference
in elevation between the suction side of the pump and the fluid surface in the reservoir (called the
suction lift or static suction head or static head), hL is the head loss in the pipeline between the
reservoir and suction side of the pump (including minor losses), and pv is the saturation vapor
pressure. In applying either Equation 2.125 or 2.126 to calculate NPSH, care must be taken to use
a consistent measure of the pressures, using either gage pressures or absolute pressures. Absolute
pressures are usually more convenient, since the vapor pressure is typically given as an absolute
pressure. A pump requires a minimum NPSH to prevent the onset of cavitation within the pump,
and this minimum NPSH is called the required net positive suction head, NPSHR, which is generally
supplied by the pump manufacturer. A typical illustration of this is shown in Figure 2.16, where
isolines of NPSRR are overlaid on the pump performance curves. In the case shown, the allowable
net positive suction head ranges from 16 ft (4.9 m) for higher flowrates down to approximately
zero, which is indicated by a bold line that meets the 55% efficiency contour.
Example 2.13.
A pump with a performance curve of hp = 12−0.01Q2
(hp in m, Q in L/s) is located 3 m above a water reservoir and
pumps water from the reservoir at a rate of 24.5 L/s through a 102-mm diameter ductile iron pipe (ks = 0.26 mm).
The length of the pipeline between the reservoir and the suction side of the pump is 3.5 m, and the temperature of
the water is 20◦
C. Calculate the available net positive suction head at the pump. If the pump manufacturer gives the
required net positive suction head under the current operating conditions as 1.2 m, determine the maximum height
above the surface of the reservoir that the pump can be located and still deliver the same flow.
Solution.
The available net positive suction head, NPSHA is given by Equation 2.126 as
NPSHA =
po
γ
− ∆zs − hL −
pv
γ
(2.127)
Atmospheric pressure, po, can be taken as 101 kPa; the specific weight of water, γ, is 9.79 kN/m3
; the suction lift,
∆zs, is 3 m; and at 20◦
C, and the saturated vapor pressure of water, pv, is 2.34 kPa. The head loss, hL, must be
estimated using the Darcy-Weisbach equation and minor loss coefficients. The flowrate, Q, is 24.5 L/s = 0.0245 m3
/s,
and the average velocity of flow in the pipe, V , is given by
V =
Q
A
=
0.0245
π
4
(0.102)2
= 3.0 m/s
At 20◦
C the kinematic viscosity, ν, is 1.00 × 10−6
m2
/s and the Reynolds number of the flow, Re, is given by
Re =
V D
ν
=
(3)(0.102)
1.00 × 10−6
= 3.06 × 105
Using Re = 3.06 × 105
, ks = 0.26 mm and D = 0.102 m, the Colebrook equation gives f = 0.0257. Assuming an
inlet head loss of V 2
/2g (for a projecting inlet), then the head loss, hL, in the pipeline between the reservoir and the
suction side of the pump is given by
hL =

1 +
fL
D

V 2
2g
=

1 +
(0.0257)(3.5)
(0.102)

(3.0)2
2(9.81)
= 0.863 m

58
Now that all the parameters necessary to calculate the available net positive suction head, NPSHA, have been
determined, Equation 2.127 gives
NPSHA =
po
γ
− zs − hL −
pv
γ
=
101
9.79
− 3 − 0.863 −
2.34
9.79
= 6.21 m
It is comforting to know that the available net positive suction head (NPSHA = 6.21 m) significantly exceeds the
required net positive suction head (NPSHR = 1.2 m).
The maximum allowable static lift occurs when NPSHA = NPSHR = 1.2 m, in which case Equation 2.127 gives
1.2 =
po
γ
− zs − hL −
pv
γ
(2.128)
where po = 101 kPa, and pv = 2.34 kPa. The head loss, hL, between the pump and the reservoir can be estimated
by the relation
hL =

1 +
f(zs + 0.5)
D

V 2
2g
where the length of the pipe from the reservoir to the pump is estimated as zs + 0.5 m, D = 0.102 m, f = 0.0257,
and V = 3.0 m/s. Therefore,
hL =

1 +
(0.0257)(zs + 0.5)
0.102

32
2(9.81)
= 0.517 + 0.116zs
Substituting this equation into Equation 2.128 gives
1.2 =
po
γ
− zs − hL −
pv
γ
=
101
9.79
− zs − (0.517 + 0.116zs) −
2.34
9.79
= 9.56 − 1.116zs
Solving for zs yields
zs = 7.49 m
Therefore, the pump should be no more than 7.49 m above the reservoir.
It is interesting to note that, although the practical limit for the suction lift is typically on the order of 7 m, difficulties
in keeping air out of the suction pipe frequently limit the suction lift to around 3 m (Kay, 1998).
2.4.4 Multiple-Pump Systems
In cases where a single pump is inadequate to achieve a desired operating condition, multiple pumps
can be used. Combinations of pumps are referred to as pump systems, and the pumps within these
systems are typically arranged either in series or parallel. The characteristic curve of a pump
system is determined by the arrangement of pumps within the system. Consider the case of two
identical pumps in series, illustrated in Figure 2.19(a). The flow through each pump is equal to Q,
and the head added by each pump is hp. For the two-pump system, the flow through the system is
equal to Q and the head added by the system is 2hp. Consequently, the characteristic curve of the
two-pump (in series) system is related to the characteristic curve of each pump in that for any flow
Q the head added by the system is twice the head added by a single pump, and the relationship
between the single-pump characteristic curve and the two-pump characteristic curve is illustrated in
Figure 2.19(b). This analysis can be extended to cases where the pump system contains n identical
pumps in series, in which case the n-pump characteristic curve is derived from the single-pump

Pump system
(a)
EGL
hp
Q
Q P
Q
P
Q
hp
(b)
Two pumps in series
One pump
hp
Q
Figure 2.19: Pumps in Series
(b)
Two pumps in parallel
One pump
hp
Q
Pump system
(a)
EGL
2Q
2Q
P
Q
P
Q
hp
Figure 2.20: Pumps in Parallel
characteristic curve by multiplying the ordinate of the single-pump characteristic curve (hp) by n.
Pumps in series are used in applications involving unusually high heads.
The case of two identical pumps arranged in parallel is illustrated in Figure 2.20. In this case,
the flow through each pump is Q and the head added is hp; therefore, the flow through the two-pump
system is equal to 2Q, while the head added is hp. Consequently, the characteristic curve of the
two-pump system is derived from the characteristic curve of the individual pumps by multiplying
the abscissa (Q) by two. This is illustrated in Figure 2.20(b). In a similar manner, the characteristic
curves of systems containing n identical pumps in parallel can be derived from the single-pump
characteristic curve by multiplying the abscissa (Q) by n. Pumps in parallel are used in cases where
the desired flowrate is beyond the range of a single pump and also to provide flexibility in pump
operations, since some pumps in the system can be shut down during low-demand conditions or
for service. This arrangement is common in sewage pump stations and water-distribution systems,
where flowrates vary significantly during the course of a day.
When pumps are placed either in series or parallel, it is usually desirable that these pumps be
identical; otherwise, the pumps will be loaded unequally and the efficiency of the pump system will
be less than optimal. In cases where nonidentical pumps are placed in series, the characteristic
curve of the pump system is obtained by summing the heads added by the individual pumps for a
given flowrate. In cases where nonidentical pumps are placed in parallel, the characteristic curve of
the pump system is obtained by summing the flowrates through the individual pumps for a given
head.

60
Example 2.14.
If a pump has a performance curve given by
hp = 12 − 0.1Q2
then what is the performance curve for: (a) a system having three of these pumps in series; and (b) a system having
three of these pumps in parallel?
Solution.
(a) For a system with three pumps in series, the same flow, Q, goes through each pump, and each pump adds
one-third of the head, Hp, added by the pump system. Therefore,
Hp
3
= 12 − 0.1Q2
and the characteristic curve of the pump system is
Hp = 36 − 0.3Q2
(b) For a system consisting of three pumps in parallel, one-third of the total flow, Q, goes through each pump,
and the head added by each pump is the same as the total head, Hp added by the pump system. Therefore
Hp = 12 − 0.1

Q
3
2
and the characteristic curve of the pump system is
Hp = 12 − 0.011Q2
2.5 Design of Water Distribution Systems
Water distribution systems move water from treatment plants to homes, offices, industries, and
other consumers. The major components of a water distribution system are pipelines, pumps,
storage facilities, valves, and meters. The primary requirements of distribution system are to
supply each customer with a sufficient volume of water at adequate pressure, to deliver safe water
that satisfies the quality expectations of customers, and to have sufficient capacity and reserve
storage for fire protection. (AWWA, 2003c).
2.5.1 Water Demand
Major considerations in designing water-supply systems are the water demands of the population
being served, the fire flows needed to protect life and property, and the proximity of the service area
to sources of water. There are usually several categories of water demand within any populated
area, and these sources of demand can be broadly grouped into residential, commercial, industrial,
and public. Residential water use is associated with houses and apartments where people live;
commercial water use is associated with retail businesses, offices, hotels, and restaurants; industrial
water use is associated with manufacturing and processing operations; and public water use includes
governmental facilities that use water. Large industrial requirements are typically satisfied by
sources other than the public water supply.
A typical distribution of water use for an average city in the United States is given in Table 2.4.
These rates vary from city to city as a result of differences in local conditions that are unrelated

Table 2.4: Typical Distribution of Water Demand
Average use Percent of
Category (liters/day)/person total
Residential 380 56
Commercial 115 17
Industrial 85 12
Public 65 9
Loss 40 6
Total 685 100
Source: Solley, 1998
to the efficiency of water use. Water consumption is frequently stated in terms of the average
amount of water delivered per day (to all categories of water use) divided by the population served,
which is called the average per capita demand. The distribution of average per capita rates among
392 water-supply systems serving approximately 95 million people in the United States is shown
in Table 2.5. The average per capita water usage in this sample was 660 L/d, with a standard
Table 2.5: Distribution of Per Capita Water Demand
Range Number of Percent of
(liters/day)/person systems systems
190–370 30 7.7
380–560 132 33.7
570–750 133 33.9
760–940 51 13.0
950–1130 19 4.8
1140 27 6.9
Source: Reprinted from 1984 Water Utility Operating
Data, by permission. Copyright c
1986 American Wa-
ter Works Association.
deviation of 270 L/d. Generally, high per capita rates are found in water-supply systems servicing
large industrial or commercial sectors (Dziegielewski et al., 1996).
In the planning of municipal water-supply projects, the water demand at the end of the design
life of the project is usually the basis for design. For existing water-supply systems, the American
Water Works Association (AWWA, 1992) recommends that every 5 or 10 years, as a minimum,
water-distribution systems be thoroughly reevaluated for requirements that would be placed on
it by development and reconstruction over a 20-year period into the future. The estimation of
the design flowrates for components of the water-supply system typically requires prediction of
the population of the service area at the end of the design life, which is then multiplied by the
per capita water demand to yield the design flowrate. Whereas the per capita water demand can
usually be assumed to be fairly constant, the estimation of the future population typically involves
a nonlinear extrapolation of past population trends.
A variety of methods are used in population forecasting. The simplest models treat the popula-

62
tion as a whole, forecast future populations based on past trends, and fit empirical growth functions
to historical population data. The most complex models disaggregate the population into various
groups and forecast the growth of each group separately. A popular approach that segregates the
population by age and gender is cohort analysis (Sykes, 1995). High levels of disaggregation have
the advantage of making forecast assumptions very explicit, but these models tend to be complex
and require more data than the empirical models that treat the population as a whole. Over rel-
atively short time horizons, on the order of 10 years, detailed disaggregation models may not be
any more accurate than using empirical extrapolation models of the population as a whole. Several
conventional extrapolation models are illustrated in the following paragraphs.
Populated areas tend to grow in at varying rates, as illustrated in Figure 2.21. In the early
5 k1P
Time, t
Population,
P
Psat
Geometric growth phase,
dP
dt
5 k2
Arithmetic growth phase,
dP
dt
5 k3(Psat 2 P )
Declining growth phase,
dP
dt
Figure 2.21: Growth Phases in Populated Areas
stages of growth, there are wide open spaces. Population, P, tends to grow geometrically according
to the relation
dP
dt
= k1P (2.129)
where k1 is a growth constant. Integrating Equation 2.129 gives the following expression for the
population as a function of time
P(t) = Poek1t
(2.130)
where Po is the population at some initial time designated as t = 0. Beyond the initial geometric
growth phase, the rate of growth begins to level off and the following arithmetic growth relation
may be more appropriate
dP
dt
= k2 (2.131)
where k2 is an arithmetic growth constant. Integrating Equation 2.131 gives the following expression
for the population as a function of time
P(t) = Po + k2t (2.132)
where Po is the population at t = 0. Ultimately, the growth of population centers becomes limited
by the resources available to support the population, and further growth is influenced by the
saturation population of the area, Psat, and the population growth is described by a relation such
as
dP
dt
= k3(Psat − P) (2.133)

where k3 is a constant. This phase of growth is called the declining growth phase. Almost all
communities have zoning regulations that control the use of both developed and undeveloped areas
within their jurisdiction (sometimes called a master plan), and a review of these regulations will
yield an estimate of the saturation population of the undeveloped areas. Integrating Equation 2.133
gives the following expression for the population as a function of time
P(t) = Psat − (Psat − Po)e−k3t
(2.134)
where Po is the population at t = 0.
The time scale associated with each growth phase is typically on the order of 10 years, although
the actual duration of each phase can deviate significantly from this number. The duration of
each phase is important in that population extrapolation using a single-phase equation can only be
justified for the duration of that growth phase. Consequently, single-phase extrapolations are typi-
cally limited to 10 years or less, and these population predictions are termed short-term projections
(Viessman and Welty, 1985). Extrapolation beyond 10 years, called long-term projections, involve
fitting an S-shaped curve to the historical population trends and then extrapolating using the fitted
equation. The most commonly fitted S-curve is the so-called logistic curve, which is described by
the equation
P(t) =
Psat
1 + aebt
(2.135)
where a and b are constants. The conventional methodology to fit the population equations to
historical data is to plot the historical data, observe the trend in the data, and fit the curve that
best matches the population trend. Regardless of which method is used to forecast the population,
errors less than 10% can be expected for planning periods shorter than 10 years, and errors greater
than 50% can be expected for planning periods longer than 20 years (Sykes, 1995).
Example 2.15.
You are in the process of designing a water-supply system for a town, and the design life of your system is to end in the
year 2020. The population in the town has been measured every 10 years since 1920 by the U.S. Census Bureau, and
the reported populations are tabulated here. Estimate the population in the town using (a) graphical extension, (b)
arithmetic growth projection, (c) geometric growth projection, (d) declining growth projection (assuming a saturation
concentration of 600,000 people), and (e) logistic curve projection.
Year Population
1920 125,000
1930 150,000
1940 150,000
1950 185,000
1960 185,000
1970 210,000
1980 280,000
1990 320,000
Solution.
The population trend is plotted in Figure 2.22, where a geometric growth rate approaching an arithmetic growth rate
is indicated.
(a) A growth curve matching the trend in the measured populations is indicated in Figure 2.22. Graphical
extension to the year 2020 leads to a population estimate of 530,000 people.

64
600
530,000
Population trend
100
1920
Year
2020
(d)
Population
(thousands)
500
400
350
300
250
200
150
2000
1980
A
B
C
1960
1940
(e)
(b)
(c)
(a)
Census data
Figure 2.22: Population Trend
(b) Arithmetic growth is described by Equation 2.132 as
P(t) = Po + k2t (2.136)
where Po and k2 are constants. Consider the arithmetic projection of a line passing through points B and C
on the approximate growth curve shown in Figure 2.22. At point B, t = 0 (year 1980) and P = 270,000; at
point C, t = 10 (year 1990) and P = 330,000. Applying these conditions to Equation 2.136 yields
P = 270000 + 6000t (2.137)
In the year 2020, t = 40 years and the population estimate given by Equation 2.137 is
P = 510,000 people
(c) Geometric growth is described by Equation 2.130 as
P = Poek1t
(2.138)
where k1 and Po are constants. Using points A and C in Figure 2.22 as a basis for projection, then at t = 0
(year 1970), P = 225,000, and at t = 20 (year 1990), P = 330,000. Applying these conditions to Equation
2.138 yields
P = 225000e0.0195t
(2.139)
In the year 2020, t = 50 years and the population estimate given by Equation 2.139 is
P = 597,000 people
(d) Declining growth is described by Equation 2.134 as
P(t) = Psat − (Psat − Po)e−k3t
(2.140)
where Po and k3 are constants. Using points A and C in Figure 2.22, then at t = 0 (year 1970), P = 225,000,
at t = 20 (year 1990), P = 330,000, and Psat = 600,000. Applying these conditions to Equation 2.140 yields
P = 600000 − 375000e−0.0164t
(2.141)
In the year 2020, t = 50 years and the population given by Equation 2.141 is given by
P = 434,800 people

(e) The logistic curve is described by Equation 2.135. Using points A and C in Figure 2.22 to evaluate the
constants in Equation 2.135 (t = 0 in 1970) yields
P =
600000
1 + 1.67e−0.0357t
(2.142)
In 2020, t = 50 years and the population given by Equation 2.142 is
P = 469,000 people
These results indicate that the population projection in 2020 is quite uncertain, with estimates ranging from
597,000 for geometric growth to 434,800 for declining growth. The projected results are compared graphically
in Figure 2.22. Closer inspection of the predictions indicate that the declining and logistic growth models are
limited by the specified saturation population of 600,000, while the geometric growth model is not limited by
saturation conditions and produces the highest projected population.
The multiplication of the population projection by the per capita water demand is used to
estimate the average daily demand for a municipal water-supply system. The (annual) average
daily demand is equal to the average of the daily demands over one year and is typically given in
m3/s.
Variations in Demand. Water demand generally fluctuates between being below the average
daily demand in the early morning hours and above the average daily demand during the midday
hours. Typical daily cycles in water demand are shown in Figure 2.23. On a typical day in most
0
50
12 a.m.
Time of day
Typical winter
day
Maximum day
for year
Percent
of
average
day
100
150
200
250
300
4 a.m. 8 a.m. Noon 4 p.m. 8 p.m. Midnight
Figure 2.23: Typical Daily Cycles in Water Demand
Source: Linsley, Ray K. et al, Water-Resources Engineering. Copyright c
1992 by The McGraw-Hill Companies.
communities, water use is lowest at night (11 p.m. to 5 a.m.) when most people are asleep. Water
use rises rapidly in the morning (5 a.m. to 11 a.m.) followed by moderate usage through midday
(11 a.m. to 6 p.m.). Use then increases in the evening (6 p.m. to 10 p.m.) and drops rather quickly
around 10 p.m. Overall, water-use patterns within a typical 24-hour period are characterized by
demands that are 25% to 40% of the average daily demand during the hours between midnight
and 6:00 a.m. and 150% to 175% of the average daily demand during the morning or evening peak
periods (Velon and Johnson, 1993).
The range of demand conditions that are to be expected in water-distribution systems are
specified by demand factors or peaking factors that express the ratio of the demand under certain

66
conditions to the average daily demand. Typical demand factors for various conditions are given in
Table 2.6, where the maximum daily demand is defined as the demand on the day of the year that
uses the most volume of water, and the maximum hourly demand is defined as the demand during
the hour that uses the most volume of water. The demand factors in Table 2.6 should serve only
Table 2.6: Typical Demand Factors
Range of Typical
Condition demand factors value
Daily average in maximum month 1.10–1.50 1.20
Daily average in maximum week 1.20–1.60 1.40
Maximum daily demand 1.50–3.00 1.80
Maximum hourly demand 2.00–4.00 3.25
Minimum hourly demand 0.20–0.60 0.30
Source: Velon and Johnson (1993). Reprinted by permission of The McGraw-Hill Companies.
as guidelines, with the actual demand factors in any one distribution system being best estimated
from local measurements. In small water systems, demand factors may be significantly higher than
those shown in Table 2.6.
Fire Demand. Besides the fluctuations in demand that occur under normal operating conditions,
water-distribution systems are usually designed to accommodate the large (short-term) water de-
mands associated with fighting fires. Although there is no legal requirement that a governing body
must size its water-distribution system to provide fire protection, the governing bodies of most
communities provide water for fire protection for reasons that include protection of the tax base
from destruction by fire, preservation of jobs, preservation of human life, and reduction of human
suffering. Flowrates required to fight fires can significantly exceed the maximum flowrates in the
absence of fires, particularly in small water systems. In fact, for communities with populations less
than 50,000, the need for fire protection is typically the determining factor in sizing water mains,
storage facilities, and pumping facilities (AWWA, 2003c). In contrast to urban water systems, many
rural water systems are designed to serve only domestic water needs, and fire flow requirements are
not considered in the design of these systems (AWWA, 2003c).
Numerous methods have been proposed for estimating fire flows, the most popular of which was
proposed by the Insurance Services Office, Inc. (ISO, 1980), which is an organization representing
the fire insurance underwriters. The required fire flow for individual buildings can be estimated
using the formula (ISO, 1980)
NFFi = CiOi(X + P)i (2.143)
where NFFi is the needed fire flow at location i, Ci is the construction factor based on the size of
the building and its construction, Oi is the occupancy factor reflecting the kinds of materials stored
in the building (values range from 0.75 to 1.25), and (X +P)i is the sum of the exposure factor (Xi)
and communication factor (Pi) that reflect the proximity and exposure of other buildings (values
range from 1.0 to 1.75). The construction factor, Ci, is the portion of the NFF attributed to the
size of the building and its construction and is given by
Ci = 220F

where Ci is in L/min; Ai (m2) is the effective floor area, typically equal to the area of the largest
floor in the building plus 50% of the area of all other floors; and F is a coefficient based on the
class of construction, given in Table 2.7.
Table 2.7: Construction Coefficient, F
Class of
construction Description F
1 frame 1.5
2 joisted masonry 1.0
3 noncombustible 0.8
4 masonry, noncombustible 0.8
5 modified fire resistive 0.6
6 fire resistive 0.6
Source: AWWA (1992).
The maximum value of Ci calculated using Equation 2.144 is limited by the following: 30,000
L/min for construction classes 1 and 2; 23,000 L/min for construction classes 3, 4, 5, and 6; and
23,000 L/min for a one-story building of any class of construction. The minimum value of Ci is
2,000 L/min, and the calculated value of Ci should be rounded to the nearest 1,000 L/min. The
occupancy factors, Oi, for various classes of buildings are given in Table 2.8. Detailed tables for
Table 2.8: Occupancy Factors, Oi
Combustibility class Examples Oi
C-1 Noncombustible steel or concrete products storage 0.75
C-2 Limited combustible apartments, churches, offices 0.85
C-3 Combustible department stores, supermarkets 1.00
C-4 Free burning auditoriums, warehouses 1.15
C-5 Rapid burning paint shops, upholstering shops 1.25
Source: Reprinted from Distribution System Requirements for Fire Protection (M31), by permission. Copyright c

1992 American Water Works Association.
estimating the exposure and communication factors, (X +P)i, can be found in AWWA (1992), and
values of (X+P)i are typically on the order of 1.4. The NFF calculated using Equation 2.143 should
not exceed 45,000 L/min, nor be less than 2,000 L/min. According to AWWA (1992), 2,000 L/min
is the minimum amount of water with which any fire can be controlled and suppressed safely and
effectively. The NFF should be rounded to the nearest 1,000 L/min if less than 9,000 L/min, and
to the nearest 2,000 L/min if greater than 9,000 L/min. For one- and two-family dwellings not
exceeding two stories in height, the NFF listed in Table 2.9 should be used. For other habitable
buildings not listed in Table 2.9, the NFF should not exceed 13,000 L/min maximum.
Usually the local water utility will have a policy on the upper limit of fire protection that it will
provide to individual buildings. Those wanting higher fire flows need to either provide their own
system or reduce fire-flow requirements by installing sprinkler systems, fire walls, or fire-retardant
materials (Walski, 1996; AWWA, 1992). Estimates of the needed fire flow calculated using Equation
2.143 are used to determine the fire-flow requirements of the water-supply system, where the needed
fire flow is calculated at several representative locations in the service area, and it is assumed that

68
Table 2.9: Needed Fire Flow for One- and Two-Family Dwellings
Distance between Needed fire
buildings (m) flow (L/min)
30 2,000
9.5–30 3,000
3.5–9.5 4,000
3.5 6,000
Source: Reprinted from Distribution System
Requirements for Fire Protection (M31), by
permission. Copyright c
1992 American Wa-
ter Works Association.
only one building is on fire at any time (Sykes, 1995). The design duration of the fire should follow
the guidelines in Table 2.10. If these durations cannot be maintained, insurance rates are typically
Table 2.10: Required Fire Flow Durations
Required fire flow Duration
(L/min) (h)
9000 2
11,000–13,000 3
15,000–17,000 4
19,000–21,000 5
23,000–26,000 6
26,000–30,000 7
30,000–34,000 8
34,000–38,000 9
38,000–45,000 10
Source: Reprinted from Distribution
System Requirements for Fire Protec-
tion (M31), by permission. Copyright
c
1992 American Water Works Associ-
ation.
increased accordingly. A more detailed discussion of the requirements for fire protection has been
published by the American Water Works Association (AWWA, 1992).
Example 2.16.
Estimate the flowrate and volume of water required to provide adequate fire protection to a 10-story noncombustible
building with an effective floor area of 8,000 m2
.
Solution.
The NFF can be estimated by Equation 2.143 as
NFFi = CiOi(X + P)i
where the construction factor, Ci, is given by
Ci = 220F
√
Ai

For the 10-story building, F = 0.8 (Table 2.7, noncombustible, Class 3 construction), and Ai = 8,000 m2
, hence
Ci = 220(0.8)
√
8000 = 16000 L/min
where Ci has been rounded to the nearest 1,000 L/min. The occupancy factor, Oi, is given by Table 2.8 as 0.75 (C-1
Noncombustible); (X + P)i can be estimated by the median value of 1.4; and hence the needed fire flow, NFF, is
given by
NFFi = (16000)(0.75)(1.4) = 17000 L/min
This flow must be maintained for a duration of four hours (Table 2.10). Hence the required volume, V , of water is
given by
V = 17000 × 4 × 60 = 4.08 × 106
L = 4080 m3
Fire hydrants are placed throughout the service area to provide either direct hose connections
for firefighting or connections to pumper trucks (also known as fire engines). A single-hose stream
is generally taken as 950 L/min, and hydrants are typically located at street intersections or spaced
60–150 m apart (McGhee, 1991). In high-value districts, additional hydrants may be necessary
in the middle of long blocks to supply the required fire flows. Fire hydrants may also be used to
release air at high points in the water-distribution system and blow off sediments at low points in
the system.
Design Flows. The design capacity of various components of the water-supply system are given
in Table 2.11, where low-lift pumps refer to low-head, high-rate units that convey the raw-water
supply to the treatment facility and high-lift pumps deliver finished water from the treatment fa-
cility into the distribution network at suitable pressures. The required capacities are based on per
person use and population projections for full development of the service area. The required capac-
ities shown in Table 2.11 consist of various combinations of the maximum daily demand, maximum
hourly demand, and the fire demand. Typically, the delivery pipelines from the water source to
the treatment plant, as well as the treatment plant itself, are designed with a capacity equal to the
maximum daily demand. However, because of the high cost of providing treatment, some utilities
have trended towards using peak flows averaged over a longer period than one day to design water
treatment plants (such as 2 to 5 days), and relying on system storage to meet peak demands above
treatment capacity. This approach has serious water quality implications and should be avoided if
possible (AWWA, 2004). The flowrates and pressures in the distribution system are analyzed under
both maximum daily plus fire demand and the maximum hourly demand, and the larger flowrate
governs the design. Pumps are sized for a variety of conditions from maximum daily to maximum
hourly demand, depending on their function in the distribution system. Additional reserve capacity
is usually installed in water-supply systems to allow for redundancy and maintenance requirements.
Example 2.17.
A metropolitan area has a population of 130,000 people with an average daily demand of 600 L/d/person. If the
needed fire flow is 20,000 L/min, estimate: (a) the design capacities for the wellfield and the water-treatment plant;
(b) the duration that the fire flow must be sustained and the volume of water that must be kept in the service
reservoir in case of a fire; and (c) the design capacity of the main supply pipeline to the distribution system.
Solution.
(a) The design capacity of the wellfield should be equal to the maximum daily demand (Table 2.11). With a
demand factor of 1.8 (Table 2.6), the per capita demand on the maximum day is equal to 1.8 × 600 = 1,080

70
Table 2.11: Design Periods and Capacities in Water-Supply Systems
Design period
Component (years) Design capacity
1. Source of supply:
River indefinite maximum daily demand
Wellfield 10–25 maximum daily demand
Reservoir 25–50 average annual demand
2. Conveyance:
Intake conduit 25–50 maximum daily demand
Conduit to treatment plant 25–50 maximum daily demand
3. Pumps:
Low-lift 10 maximum daily demand, one reserve unit
High-lift 10 maximum hourly demand, one reserve unit
4. Treatment plant 10–15 maximum daily demand
5. Service reservoir 20–25 working storage plus fire demand
plus emergency storage
6. Distribution system:
Supply pipe or conduit 25–50 greater of (1) maximum daily demand plus
fire demand, or (2) maximum hourly
demand
Distribution grid full development same as for supply pipes
Source: Reprinted by permission of Waveland Press, Inc. from R. S. Gupta, Hydrology and Hydraulic Systems, Second
Edition. (Prospect Heights, IL; Waveland Press, Inc., 2001). All rights reserved.
L/day/person. Since the population served is 130,000 people, the design capacity of the wellfield, Qwell, is
given by
Qwell = 1080 × 130000 = 1.4 × 108
L/d = 1.62 m3
/s
The design capacity of the water-treatment plant is also equal to the maximum daily demand, and therefore
should also be taken as 1.62 m3
/s.
(b) The needed fire flow, Qfire, is 20000 L/min = 0.33 m3
/s. According to Table 2.10, the fire flow must be
sustained for 5 hours. The volume, Vfire, required for the fire flow will be stored in the service reservoir and is
given by
Vfire = 0.33 × 5 × 3600 = 5,940 m3
(c) The required flowrate in the main supply pipeline is equal to the maximum daily demand plus fire demand or
the maximum hourly demand, whichever is greater.
Maximum daily demand + fire demand = 1.62 + 0.33 = 1.95 m3
/s
Maximum hourly demand =
3.25
1.80
× 1.62 = 2.92 m3
/s
where a demand factor of 3.25 has been assumed for the maximum hourly demand. The main supply pipe to
the distribution system should therefore be designed with a capacity of 2.92 m3
/s. The water pressure within
the distribution system must be above acceptable levels when the system demand is 2.92 m3
/s.

2.5.2 Pipelines
Water-distribution systems typically consist of connected pipe loops throughout the service area.
Pipelines in water-distribution systems include transmission lines, arterial mains, and distribution
mains. Transmission lines carry flow from the water-treatment plant to the service area, typically
have diameters greater than 600 mm, and are usually on the order of 3 km apart. Arterial mains
are connected to transmission mains and are laid out in interlocking loops with the pipelines not
more than 1 km apart and diameters in the range of 400–500 mm. Smaller form a grid over the
entire service area, with diameters in the range of 150–300 mm, and supply water to every user.
Pipelines in distribution systems are collectively called water mains, and a pipe that carries water
from a main to a building or property is called a service line. Water mains are normally installed
within the rights-of-way of streets. Dead ends in water-distribution systems should be avoided
whenever possible, since the lack of flow in such lines may contribute to water-quality problems.
Pipelines in water-distribution systems are typically designed with constraints relating to the
minimum pipe size, maximum allowable velocity, and commercially available materials that will
perform adequately under operating conditions.
Minimum Size. The size of a water main determines its carrying capacity. Main sizes must be
selected to provide the capacity to meet peak domestic, commercial, and industrial demands
in the area to be served, and must also provide for fire flow at the necessary pressure. For
fire protection, insurance underwriters typically require a minimum main size of 150 mm
for residential areas and 200 mm for high-value districts (such as sports stadiums, shopping
centers, and libraries) if cross-connecting mains are not more than 180 m apart. On principal
streets, and for all long lines not connected at frequent intervals, 300-mm and larger mains
are required.
Service Lines. Service lines are pipes, including accessories, that carry water from the main to
the point of service, which is normally a meter setting or curb stop located at the property
line. Service lines can be any size, depending on how much water is required to serve a
particular customer. Single-family residences are most commonly served with 20-mm (3/4
in.) diameter service lines, while larger residences and buildings located far from the main
connection should have a 25-mm (1 in.) or larger service line. To properly size service lines
it is essential to know the peak demands than any service tap will be called on to serve.
A common method to estimate service flows is to sum the fixture units associated with the
number and type of fixtures served by the service line and then use a curve called the Hunter
curve to relate the peak flowrate to total fixture units. This relationship is included in
most local plumbing codes and is contained in the Uniform Plumbing Code (UPC). Recent
research has indicated that the peak flows estimated from fixture units and the Hunter curve
provide conservative estimates of peak flows (AWWA, 2004). Irrigation demands that occur
simultaneously with peak domestic demands must be added to the estimated peak domestic
demands. Service lines are sized to provide an adequate service pressure downstream of the
water meter when the service line is delivering the peak flow. This requires that the pressure
and elevation at the tap, length of service pipe, head loss at the meter, elevation at the
water meter, valve losses, and desired pressure downstream of the meter be known. Using
the energy equation, the minimum service line diameter is calculated using this information.
It is usually better to overdesign a service line than to underdesign a service line because of

72
the cost of replacing a service line if service pressures turn out to be inadequate. To prevent
water hammer, velocities greater than 3 m/s should be avoided. Materials used for service-
line pipe and tubing are typically either copper (tubing) or plastic, which includes polyvinyl
chloride (PVC) and polyethylene (PE). Type K copper is the most commonly used material
for copper service lines. Older service lines used lead and galvanized iron, which are no longer
recommended. The valve used to connect a small-diameter service line to a water main is
called a corporation stop, which is sometimes loosely referred to as the corporation cock,
corporation tap, corp stop, corporation, or simply corp or stop (AWWA, 2003c). Tapping
a water main and inserting a corporation stop directly into the pipe wall requires a tapping
machine, and taps are typically installed at the 10 or 2 o’clock position on the pipe. Guidelines
for designing water service lines and meters are given in AWWA Manual M22 (AWWA, 2004).
Good construction practices must be used when installing service lines to avoid costly repairs
in the future. This must include burying the pipe below frost lines, maintaining proper ditch
conditions, proper backfill, trench compaction, and protection from underground structures
that may cause damage to the ppe.
Allowable Velocities. Maximum allowable velocities in pipeline systems are imposed to control
friction losses and hydraulic transients. Maximum allowable velocities of 0.9 to 1.8 m/s
are common in water-distribution pipes, and the American Water Works Association recom-
mends a limit of about 1.5 m/s under normal operating conditions, but velocities may exceed
this guideline under fire-flow conditions (AWWA, 2003c). The importance of controlling the
maximum velocities in water distribution systems is supported by the fact that a change in
velocity of 0.3 m/s in water transmission and distribution systems can increase the pressure
in a pipe by approximately 345 kPa, while the standard design for DIP includes only a 690
kPa allowance (AWWA, 2003d).
Material. Pipeline materials should generally be selected based on a consideration of service con-
ditions, availability, properties of the pipe, and economics. In selecting pipe materials the
following considerations should be taken into account:
• Most water distribution mains in older cities in the United States are made of (gray)
cast iron pipe (CIP), with many cities having CIP over 100 years old and still providing
satisfactory service (Mays, 2000; AWWA, 2003d). CIP is no longer manufactured in the
United States.
• For new distribution mains, ductile iron pipe (DIP) is most widely used for pipe diam-
eters up to 760 mm (30 in.), and it has largely replaced CIP in new construction. DIP
has all the good qualities of CIP plus additional strength and ductility. DIP is manufac-
tured in diameters from 76 to 1625 mm (3–64 in.). For diameters from 100 to 500 mm
(4–20 in.), standard commercial sizes are available in 50-mm (2 in.) increments, while
for diameters from 600 to 1200 mm (24–48 in.), the size increments are 150 mm (6 in.).
The standard lengths of DIP are 5.5 m (18 ft) and 6.1 m (20 ft). DIP is usually coated
(outside and inside) with an bituminous coating to minimize corrosion. An internal
cement-mortar lining 1.5 - 3 mm thick is common, and external polyethylene wraps are
used to reduce corrosion in corrosive soil environments. DIP used in water systems in
the United States are provided with a cement-mortar lining unless otherwise specified
by the purchaser. The design of DIP and fittings are covered in AWWA Manual M41

(AWWA, 2003d) and guidance for DIP lining is covered in AWWA Standard C105 (lat-
est edition). Tests conducted by the Ductile Iron Pipe Research Association (DIPRA)
suggest a Hazen-Williams C-value of 140 is appropriate for the design of cement-mortar
lined DIP. A variety of joints are available for use with DIP, which includes push-on
(the most common), mechanical, flanged, ball-and-socket, and numerous joint designs.
A stack of DIP is shown in Figure 2.24, and the the bell and spigot pipe ends that
facilitate push-on connection are apparent. A rubber gasket, to ensure a tight fit, is
contained in the bell side of the pipe.
Figure 2.24: Ductile Iron Pipe
• Steel pipe usually compares favorably with DIP for diameters larger than 400 mm (16
in.) As a consequence, steel pipe is primarily used for transmission lines in water distri-
bution systems. Steel pipe available in diameters from 100 to 3600 mm (4–144 in.). The
standard length of steel pipe is 12.2 m (40 ft).The interior of steel pipe is usually pro-
tected with either cement mortar or epoxy, and the exterior is protected by a variety of
plastic coatings, bituminous materials, and polyethylene tapes depending on the degree
of protection required. Guidance for the design of steel pipe are covered in AWWA Man-
ual M11 (latest edition), and linings for steel pipe are covered under AWWA Standard
C205 (latest edition) and AWWA Standard C210 (latest edition).
• Plastic materials used for fabricating water main pipe include polyvinyl chloride (PVC),
polyethylene (PE), and polybutylene (PB). PVC pipe is by far the most widely used type
of plastic pipe material for small-diameter water mains. The American Water Works
Association standard (C900) for PVC pipe in sizes from 100 mm to 300 mm and laying
lengths of 6.1 m (20 ft) is based on the same outside diameter as for DIP. In this way,
standard DIP fittings can be used with PVC pipe. PVC pipe is commonly available in
diameters from 100 to 914 mm. Extruded PE and PB pipe are primarily used for water
service pipe in small sizes, however, the use of PB has decreased remarkably because
of structural difficulties caused by premature pipe failures. Research has documented
that pipe materials such as PVC, PE, and PB may be subject to permeation by lower
molecular weight organic solvents or petroleum products (AWWA, 2002b). If a water

74
pipe must pass through an area subject to contamination, caution should be used is
selecting PVC, PE, and PB pipes. In the hydraulic design of PVC pipes, a roughness
height of 0.0015 mm or a Hazen-Williams C-value of 150 are appropriate for design
(AWWA, 2002b). Details of large-diameter PE pipe are found in AWWA Standard
C906 (latest edition) and information on PVC water main pipe is available in AWWA
Manual M23 (2002b).
• Asbestos-cement (A-C) pipe has been widely installed in water distribution systems,
especially in areas where metallic pipe is subject to corrosion, such as in coastal areas.
It has also been installed in remote areas where its light weight makes it much easier
to install than CIP. Common diameters are in the range of 100 to 890 mm. The U.S.
Environmental Protection Agency banned most uses of asbestos in 1989 and, due to the
manufacturing ban, new A-C pipe is no longer being installed in the United States.
• Fiberglass pipe is available for potable water used is sizes from 25 to 3600 mm. Ad-
vantages of fiberglass pipe include corrosion resistance, light weight, low installation
cost, ease of repair, and hydraulic smoothness. Disadvantages include susceptibility
to mechanical damage, low modulus of elasticity, and lack of standard joining system.
Fiberglass pipe is covered in AWWA Standard C950 (latest edition).
• The use of concrete pressure pipe has grown rapidly since 1950. The pipe provides
a combination of the high tensile strength of steel and the high compressive strength
and corrosion resistance of concrete. The pipe is available in diameters ranging from
250 to 6400 mm and in standard lengths from 3.7 to 12.2 m. The design of concrete
pressure pipe is covered in AWWA Manual M9 (latest edition). Concrete pipe is available
with various types of liners and reinforcement, and the four types in common use in the
United States and Canada are: prestressed concrete cylinder pipe, bar-wrapped concrete
cylinder pipe, reinforced concrete cylinder pipe, and reinforced concrete noncylinder pipe.
The manufacture of prestressed concrete cylinder pipe is covered under AWWA Standard
C301 (latest edition) and AWWA Standard C304 (latest edition), bar-wrapped concrete
cylinder pipe is covered under AWWA Standard C303 (latest edition), reinforced concrete
cylinder pipe is covered under AWWA Standard C300 (latest edition), and reinforced
concrete noncylinder pipe is covered under AWWA Standard C302 (latest edition).
Pipelines in water-distribution systems should be buried to a depth below the frost line in northern
climates and at a depth sufficient to cushion the pipe against traffic loads in warmer climates
(Clark, 1990). Generally, a cover of 1.2 m to 1.5 m is used for large mains and 0.75 m to 1.0 m
for smaller mains. In areas where frost penetration is a significant factor, mains can have as much
as 2.5 m of cover. Trenches for water mains should be as narrow as possible and still be wide
enough to allow for proper joining and compaction around the pipe. The suggested trench width
is the nominal pipe diameter plus 0.6 m; in deep trenches, sloping may be necessary to keep the
bank from caving in. Trench bottoms should be undercut 15 to 25 cm, and sand, clean fill, or
crushed stone installed to provide a cushion against the bottom of the excavation, which is usually
rock (Clark, 1990). Standards for pipe construction, installation, and performance are published
by the American Water Works Association in its C-series standards, which are continuously being
updated.

2.5.3 Pumps
Service pressures are typically maintained by pumps, with head losses and increases in pipeline
elevations acting to reduce pressures and decreases in pipeline elevations acting to increase pressures.
When portions of the distribution system are separated by long distances or significant changes
in elevation, booster pumps are sometimes used to maintain acceptable service pressures. In some
cases, fire-service pumps are used to provide additional capacity for emergency fire protection.
Pumps operate at the intersection of the pump performance curve and the system curve. Since the
system curve is significantly affected by variations in water demand, there is a significant variation
in pump operating conditions. In most cases, the range of operating conditions is too wide to be
met by a single pump, and multiple-pump installations or variable speed pumps are required (Velon
and Johnson, 1993).
2.5.4 Valves
Valves in water distribution systems are designed to perform several different functions, and the
primary functions are to start and stop flow, isolate piping, regulate pressure and throttle flow,
prevent backflow, and relieve pressure. Shutoff valves or gate valves are typically provided at 350-
m intervals so that areas within the system can be isolated for repair or maintenance; air-relief
valves or air-and-vacuum relief valves are required at high points to release trapped air; blowoff
valves or drain valves may be required at low points; and backflow prevention devices are required
by applicable regulations to prevent contamination from backflows of nonpotable water into the
distribution system from system outlets. To maintain the performance of water-distribution systems
it is recommended that each valve should be operated through a full cycle and then returned to its
normal position on a regular schedule. The time interval between operations should be determined
by the manufacturer’s recommendations, size of the valve, severity of the operating conditions, and
the importance of the installation (AWWA, 2003d).
2.5.5 Meters
The water meter s a changeable component of a customer’s water system. Unlike the service line and
water tap, whic when incorrectly sized will generally require expensive excavation and retapping,
water meters can usually be changed less expensively. Selection of the type and size of a meter
should be based primarily on the range of flow, and the pressure loss through the meter should
also be a consideration. For many single-family residences, a 20-mm service line with a 15-mm
meter is typical, while in areas where irrigation is prevalent, 20-mm or 25-mm meter may be more
prevalent. Undersizing the meter can cause pressure-related problems, and oversizing the meter can
result in reduced revenue and inaccurate meter recordings (since the flows do not register). Some
customers such as hospitals, schools, and factories with processes requiring uninterrupted water
service should have bypasses installed around the meter so that meter test and repair activities can
be performed at scheduled intervals without inconvenience to either the customer or the utility.
The bypass should be locked and valved appropriately.
2.5.6 Fire Hydrants
Fire hydrants are one of the few parts of a water distribution system that are visible to the public,
so keeping them well maintained can help a water utility project a good public image. Fire hydrants

76
are direct connections to the water mains and, in addition to providing an outlet for fire protection,
fire hydrants are used for flushing water mains, flushing sewers, filling tank trucks for street washing,
tree spraying, and providing a temporary water source for construction jobs. A typical fire hydrant
is shown in Figure 2.25, along with the pipe connection between the water main and the fire hydrant.
The vertical pipe connecting the water main to the fire hydrant is commonly called the riser. The
Figure 2.25: Fire Hydrant and Connection to Water Main
water utility is usually responsible for keeping hydrants in working order, although fire departments
sometime assume this responsibility. Standard practice is to install hydrants only on mains 150
mm or larger, however, larger mains are often necessary to ensure that the residual pressure during
fire flow remains greater than 140 kPa. Guidelines for the placement of hydrants are as follows
(AWWA, 2003c):
• Not too close to buildings since fire fighters will not position their fire (pumper) trucks where
a building wall could fall on them.
• Preferably located near street intersections, where the hose can be strung to fight a fire in
any of several directions.
• Far enough from a roadway to minimize the danger of them being struck by vehicles.
• Close enough to the pavement to ensure a secure connection with the pumper and hydrant
without the risk of the truck getting stuck in mud or snow.
• In areas of heavy snow, hydrants must be located where they are least liable to be covered
by plowed snow or struck by snow-removal equipment.
• Hydrants should be high enough off the ground that valve caps can be removed with a
standard wrench, without the wrench hitting the ground.
Fire hydrants should be inspected and operated through a full cycle on a regular schedule, and the
hydrant should be flushed to prevent sediment buildup in the hydrant or connecting piping.
2.5.7 Water Storage Reservoirs
Water usually enters the system at a fairly constant rate from the treatment plant. To accommodate
fluctuations in demand, a storage reservoir is typically located at the head of the system to store
the excess water during periods of low demand and provide water from storage during periods of

high demand. In addition to the operational storage required to accommodate diurnal (24-hour
cycle) variations in water demand, storage facilities are also used to provide storage to fight fires, to
provide storage for emergency conditions, and to equalize pressures in water-distribution systems.
Storage facilities are classified as either ground storage, elevated storage, or standpipes. The
function and relative advantages of these types of systems are as follows:
Elevated-Storage Tanks. Elevated storage tanks are constructed above ground such that the
height of the water in the elevated storage tank is sufficient to deliver water to the distribution
system at the required pressure. The storage tank is generally supported by a steel or concrete
tower, the tank is directly connected to the distribution system through a pipe called a riser,
the water level in the storage tank is equal to the elevation of the hydraulic grade line in
the distribution system (at the outlet of the storage tank), and the elevated storage tank is
said to float on the system. Elevated storage is useful in the case of fires and emergency
conditions since pumping of water from elevated tanks is not necessary, although the water
must generally be pumped into elevated storage tanks. Occasionally, system pressure could
become so high that the tank would overflow, and therefore altitude valves must be installed
on the tank fill line to keep the tank from overflowing. Elevated tanks are usually made of
steel.
Ground-Storage Reservoirs. Ground-storage reservoirs are constructed at or below ground
level and usually discharge water to the distribution system through pumps. These systems,
which are sometimes referred to simply as distribution-system reservoirs or ground-level tanks,
are usually used where very large quantities of water must be stored or when an elevated tank
is objectionable to the public. When a ground-level or buried reservoir is located at a low
elevation on the distribution system, water is admitted through a remotely operated valve,
and a pump station is provided to transfer water into the distribution system. Completely
buried reservoirs are often used where an above-ground structure is objectionable, such as
in a residential neighborhood. In some cases, the land over a buried reservoir can be used
for recreational facilities such as a ball field or tennis court. Ground-storage reservoirs are
typically constructed of steel or concrete.
Standpipes. A tank that rests on the ground with a height that is greater than its diameter is
generally referred to as a standpipe. In most installations, only water in the upper portion
of the tank will furnish usable system pressure, so most larger standpipes are equipped with
an adjacent pumping system that can be used in an emergency to pump water to the system
from the lower portion of the tank. Standpipes combine the advantages of elevated storage
with the ability to store large quantities of water, and standpipes are usually constructed
of steel. Standpipes taller than 15 m are usually uneconomical, since for taller standpipes it
tends to be more economical to build an elevated tank than to accommodate the dead storage
that must be pumped into the system.
Storage facilities in a distribution system are required to have sufficient volume to meet the following
criteria (Velon and Johnson, 1993): (1) adequate volume to supply peak demands in excess of the
maximum daily demand using no more than 50% of the available storage capacity; (2) adequate
volume to supply the critical fire demand in addition to the volume required for meeting the
maximum daily demand fluctuations; and (3) adequate volume to supply the average daily demand
of the system for the estimated duration of a possible emergency. Conventional design practice

78
is to rely on pumping to meet the daily operational demands up to the maximum daily demand;
where detailed demand data are not available, the storage available to supply the peak demands
should equal 20% to 25% of the maximum daily demand volume. Sizing the storage volume for
fire protection is based on the product of the critical fire flow and duration for the service area.
In extremely large systems where fire demands be only a small fraction of the maximum daily
demand fire storage may not be necessary (Walski, 2000). Emergency storage is generally necessary
to provide water during power outages, breaks in water mains, problems at treatment plants,
unexpected shutdowns of water-supply facilities, and other sporadic events. Emergency volumes
for most municipal water-supply systems vary from one to two days of supply capacity at the average
daily demand. The recommended standards for water works developed by the Great Lakes Upper
Mississippi River Board of State Public Health and Environmental Managers suggest a minimum
emergency storage capacity equal to the average daily system demand.
In cases where elevated storage tanks are used, the minimum acceptable height of water in an
elevated storage tank is determined by computing the minimum acceptable piezometric head in
the service area and then adding to that figure an estimate of the head losses between the critical
service location and the location of the elevated service tank, under the condition of average daily
demand. The maximum height of water in the elevated tank is then determined by adding the
minimum acceptable piezometric head to the head loss between the tank location and the critical
service location under the condition of maximum hourly demand. The difference between the calcu-
lated minimum and maximum heights of water in the elevated storage tank is then specified as the
normal operating range within the tank. The normal operating range for water in elevated tanks is
usually limited to 4.5 to 6 meters, so that fluctuations in pressure are limited to 35 to 70 kPa. In
most cases, the operating range is located in the upper half of the storage tank, with storage in the
lower half of the tank reserved for firefighting and emergency storage. Any water stored in elevated
tanks less than 14 m (46 ft) above ground is referred to as ineffective storage (Walski et al., 1990)
since the pressure in connected distribution pipes will be less than the usual minimum acceptable
pressure during emergency conditions of 140 kPa (20 psi). Operational storage in elevated tanks is
normally at elevations of more than 25 m (81 ft) above the ground, since under these conditions the
pressure in connected distribution pipes will exceed the usual minimum acceptable pressure during
normal operations of 240 kPa (35 psi). A typical elevated storage tank is illustrated in Figure 2.26.
These types of storage facilities generally have only a single pipe connection to the distribution
system, and this single pipe handles both inflows and outflows from the storage tank. This piping
arrangement is in contrast to ground storage reservoirs, which have separate inflow and outflow
piping. The inflow piping delivers the outflow from the water-treatment facility to the reservoir,
while the outflow piping delivers the water from the reservoir to the pumps that input water into
the distribution system. Elevated tanks are generally made of steel (Walski, 1996), and the largest
elevated storage tank in the United States (as of 2000) has a volume of 15,520 m3 (ASCE, 2000).
Elevated storage tanks are best placed on the downstream side of the largest demand from the
source, with the advantages that: (1) if a pipe breaks near the source, the break will not result
in disconnecting all the storage from the customers; and (2) if flow reaches the center of demand
from more than one direction, the flow carried by any individual pipe will be lower and pipe sizes
will generally be smaller, with associated cost savings (Walski, 2000). If there are multiple stor-
age tanks in the distribution system, the tanks should be placed roughly the same distance from
the source or sources, and all tanks should have approximately the same overflow elevation (other-
wise, it may be impossible to fill the highest tank without overflowing or shutting off the lower tanks.

Figure 2.26: Elevated Storage Tank
Example 2.18.
A service reservoir is to be designed for a water-supply system serving 250,000 people with an average demand of 600
L/d/capita, and a needed fire flow of 37,000 L/min. Estimate the required volume of service storage.
Solution.
The required storage is the sum of three components: (1) volume to supply the demand in excess of the maximum
daily demand, (2) fire storage, and (3) emergency storage.
The volume to supply the peak demand can be taken as 25% of the maximum daily demand volume. Taking the
maximum daily demand factor as 1.8 (Table 2.6), then the maximum daily flowrate, Qm, is given by
Qm = (1.8)(600)(250000) = 2.7 × 108
L/d = 2.7 × 105
m3
/d
The storage volume to supply the peak demand, Vpeak, is therefore given by
Vpeak = (0.25)(2.7 × 105
) = 67500 m3
According to Table 2.10, the 37,000 L/min (= 0.62 m3
/s) fire flow must be maintained for at least 9 hours. The
volume to supply the fire demand, Vfire, is therefore given by
Vfire = 0.62 × 9 × 3600 = 20100 m3
The emergency storage, Vemer, can be taken as the average daily demand, in which case
Vemer = 250000 × 600 = 150 × 106
L = 150,000 m3
The required volume, V , of the service reservoir is therefore given by
V = Vpeak + Vfire + Vemer
= 67500 + 20100 + 150000
= 237,600 m3
The service reservoir should be designed to store 238,000 m3
of water. This large volume will require a ground storage
tank (recall that the largest elevated-tank volume in the United States is 15,520 m3
), and it is interesting to note
that most of the storage in the service reservoir is reserved for emergencies.
Example 2.19.
A water-supply system is to be designed in an area where the minimum allowable pressure in the distribution system

80
is 300 kPa. A hydraulic analysis of the distribution network under average daily demand conditions indicates that the
head loss between the low-pressure service location, which has a pipeline elevation of 5.40 m, and the location of the
elevated storage tank is 10 m. Under maximum hourly demand conditions, the head loss between the low-pressure
service location and the elevated storage tank is 12 m. Determine the normal operating range for the water stored in
the elevated tank.
Solution.
Under average demand conditions, the elevation zo of the hydraulic grade line (HGL) at the reservoir location is
given by
zo =
pmin
γ
+ zmin + hL
where pmin = 300 kPa, γ = 9.79 kN/m3
, zmin = 5.4 m, and hL = 10 m, which yields
zo =
300
9.79
+ 5.4 + 10 = 46.0 m
Under maximum hourly demand conditions, the elevation z1 of the HGL at the service reservoir is given by
z1 =
300
9.79
+ 5.4 + 12 = 48.0 m
Therefore, the operating range in the storage tank should be between elevations 46.0 m and 48.0 m.
It is important to keep in mind that the best hydraulic location and most economical design
are not always the deciding factors in the location of an elevated tank. In some cases, the only
acceptable location will be in an industrial area or public park. In cases where public feeling is
very strong, a water utility may have to construct ground-level storage, which is more aesthetically
acceptable.
2.5.8 Performance Criteria for Water-Distribution Systems
The primary functions of water-distribution systems (Zipparro and Hasen, 1993) are to (1) meet
the water demands of users while maintaining acceptable pressures in the system; (2) supply water
for fire protection at specific locations within the system, while maintaining acceptable pressures
for normal service throughout the remainder of the system; and (3) provide a sufficient level of
redundancy to support a minimum level of reliable service during emergency conditions, such as
an extended loss of power or a major water-main failure. Real-time operation of water distribution
systems are typically based on remote measurements of pressures and storage-tank water levels
within the distribution system. The pressure and water-level data are typically transmitted to a
central control facility via telemetry, and adjustments to the distribution system are made from
the central facility by remote control of pumps and valves within the distribution system. These
electronic control systems are generally called supervisory control and data acquisition (SCADA)
systems (Chase, 2000). Operating criteria for service pressures and storage facilities are described
below.
The requirement that adequate pressures be maintained in the distribution system while sup-
plying the service demands requires that the system be analyzed on the basis of allowable pres-
sures. Minimum acceptable pressures are necessary to prevent contamination of the water supply
from cross-connections. Criteria for minimum acceptable service pressures recommended by the
Great Lakes Upper Mississippi River Board of State Public Health and Environmental Managers
(GLUMB, 1987) and endorsed by the American Water Works Association (AWWA, 2003c) are
typical of most water-distribution systems, and they are listed in Table 2.12. During main breaks,

Table 2.12: Minimum Acceptable Pressures in Distribution Systems
Minimum acceptable pressure
Demand condition (kPa)
Average daily demand 240–410
Maximum daily demand 240–410
Maximum hourly demand 240–410
Fire situation 140
Emergency conditions 140
Source: GLUMB (1987).
when the pressure in water-supply pipelines can drop below 140 kPa, it is not uncommon for a
water utility to issue a “boil water” advisory because of the possibility of system contamination
from cross connections (Chase, 2000). There are several considerations in assessing the adequacy
of service pressures, including (1) the pressure required at street level for excellent flow to a 3-story
building is about 290 kPa; (2) flow is adequate for residential areas if the pressure is not reduced
below 240 kPa; (3) the pressure required for adequate flow to a 20-story building is about 830 kPa,
which is not desirable because of the associated leakage and waste; (4) very tall buildings are usu-
ally served with their own pumping equipment; and (5) it is usually desirable to maintain normal
pressures of 410–520 kPa since these pressures are adequate for the following purposes:
• To supply ordinary consumption for buildings up to 10 stories.
• To provide adequate sprinkler service in buildings of 4 to 5 stories.
• To provide direct hydrant service for quick response.
• To allow larger margin for fluctuations in pressure caused by clogged pipes and excessive
length of service pipes.
Pressures higher than 650 kPa should be avoided if possible because of excessive leakage and
water use, and the added burden of installing and maintaining pressure-reducing valves and other
specialized equipment (Clark, 1990). Customers do not generally like high pressure because water
comes out of a quickly-opened faucet with too much force (AWWA, 2003c). In addition, excessive
pressures decrease the the life of water heaters and other plumbing fixtures.
2.5.9 Water Quality
The quality of water delivered to consumers can be significantly influenced by various components
of a water distribution system. The principal factors affecting water quality in distribution systems
are the quality of the treated water fed to the system; the material and condition of the pipes, valves,
and storage facilities that make up the system; and the amount of time that the water is kept in
the system (Grayman et al., 2000; AWWA, 2003c). Key processes that affect water quality within
the distribution system usually include the loss of disinfection residual with resulting microbial
regrowth, and the formation of disinfection byproducts such as trihalomethanes. Water-quality
deterioration is often proportional to the time the water is resident in the distribution system. The
longer the water is in contact with the pipe walls and is held in storage facilities, the greater the

82
opportunity for water-quality changes. Generally, a hydraulic detention time of less than 7 days in
the distribution system is recommended (AWWA, 2003c).
The velocity of flow in most mains is normally very low because mains are designed to handle
fire flow, which may be several times larger than domestic flow. As a result, corrosion products
and other solids tend to settle on the pipe bottom, and this problem is especially bad in dead-end
mains or in areas of low water consumption. These deposits can can be a source of color, odor,
and taste in the water when the deposits are stirred up by an increase in flow velocity or a reversal
of flow in the distribution system. To prevent these sediments from accumulating and causing
water-quality problems, pipe flushing is a typical maintenance routine. Flushing involves opening
a hydrant located near the problem area, and the hydrant should be kept open as long as needed to
flush out the sediment, which typically requires the removal of up to three pipe volumes (AWWA,
2003c). Only through experience will an operator be able to how often or how long certain areas
should be flushed. Some systems find that dead-end mains must be flushed as often as weekly to
avoid customer complaints of rusty water. The flow required for effective flushing is in the range of
0.75 - 1.1 m/s, with velocities limited to less than 3.1 - 3.7 m/s to avoid excessive scouring (AWWA,
2003c). If flushing proves to be inadequate for cleaning mains, air purging or cleaning devices such
as swabs or pigs may need to be used.
In recognition of the influence of the water distribution system on water quality, water quality
regulations in the United States requires that water to be sampled at at the entry point to the distri-
bution system, at various points within the distribution system, and at consumers’ taps (Kirmeyer
et al., 1999). The computer program EPANET (Rossman, 2000) is widely used to simulate the
water quality in distribution networks.
2.5.10 Network Analysis
Methodologies for analyzing pipe networks were discussed in Section 2.3, and these methods can be
applied to any given pipe network to calculate the pressure and flow distribution under a variety of
demand conditions. In complex pipe networks, the application of computer programs to implement
these methodologies is standard practice (Haestad Methods Inc., 1997a; 1997b; 2002)). Computer
programs allow engineers to easily calculate the hydraulic performance of complex networks and
such parameters as the age of water delivered to consumers and also to trace the origin of the
delivered water. Water age is measured from the time the water enters the system and gives an
indication of the overall quality of the delivered water. Steady-state analyses are usually adequate
for assessing the performance of various components of the distribution system, including the
pipelines, storage tanks, and pumping systems, while time-dependent simulations are useful in
assessing the response of the system over short time periods (days or less), evaluating the operation
of pumping stations and variable-level storage tanks, performing energy consumption and cost
studies, and water quality modeling (Velon and Johnson, 1993; Haestad Methods, Inc., 2002).
Modelers frequently refer to time-dependent simulations as extended-period simulations, and several
examples can be found in Larock et al. (2000).
An important part of analyzing large water-distribution systems is the skeletonizing of the
system, which consists of representing the full water-distribution system by a subset of the system
that includes only the most important elements. For example, consider the case of a water supply to
the subdivision shown in Figure 2.27(a), where the system shown includes the service connections to
the houses. A slight degree of skeletonization could be achieved by omitting the household service

(a) (b)
(c) (d)
Figure 2.27: Skeletonizing a Water-Distribution System
Source: Haestad Methods, 1997 Practical Guide: Hydraulics and Hydrology p. 61–62. Copyright c
1997 by Haestad
Methods, Inc. Reprinted by permission.
pipes (and their associated head losses) from consideration and accounting for the water demands
at the tie-ins and as shown in Figure 2.27(b). This reduces the number of junctions from 48 to 19.
Further skeletonization can be achieved by modeling just 4 junctions, consisting of the ends of the
main piping and the major intersections shown in Figure 2.27(c). In this case, the water demands
are associated with the nearest junctions to each of the service connections, and the dashed lines
in Figure 2.27(c) indicate the service areas for each junction. A further level of skeletonization is
shown in Figure 2.27(d), where the water supply to the entire subdivision is represented by a single
node, at which the water demand of the subdivision is attributed.
Clearly, further levels of skeletonization could be possible in large water-distribution systems.
As a general guideline, larger systems permit more degrees of skeletonization without introducing
significant error in the flow conditions of main distribution pipes.
The results of a pipe-network analysis should generally include pressures and/or hydraulic grade
line elevations at all nodes, flow, velocity, and head loss through all pipes as well as rates of flow
into and out of all storage facilities. These results are used to assess the hydraulic performance
and reliability of the network, and they are to be compared with the guidelines and specifications
required for acceptable performance.
2.6 Computer Models
Several good computer models are available for simulating flow in closed conduits, with the majority
of these models developed primarily for computing flows and pressure distributions in water-supply
networks. In engineering practice, the use of computer models to apply the fundamental principles

84
covered in this chapter is usually essential. In choosing a model for a particular application, there
are usually a variety of models to choose from, however, in doing work that is to be reviewed by
regulatory bodies, models developed and maintained by agencies of the United States government
have the greatest credibility and, perhaps more importantly, are almost universally acceptable in
supporting permit applications and defending design protocols. A secondary guideline in choosing
a model is that the simplest model that will accomplish the design objectives should be given the
most serious consideration.
EPANET. EPANET is a water-distribution-system modeling package developed by the U.S. En-
vironmental Protection Agency’s Water Supply and Water Resources Division. It performs
extended-period simulation of hydraulic and water-quality behavior within pressurized pipe
networks. A more detailed description of EPANET can be found in Rossman (2000), and the
program can be downloaded from the World Wide Web at www.epa.gov/ORD/NRMRL/wswrd/epanet.html.
Summary
The hydraulics of flow in closed conduits is the basis for designing water-supply systems and
other systems that involve the transport of water under pressure. The fundamental relationships
governing flow in closed conduits are the conservation laws of mass, momentum, and energy; the
forms of these equations that are most useful in engineering applications are derived from first
principles. Of particular note is the momentum equation, the most useful form of which is the
Darcy-Weisbach equation. Techniques for analyzing flows in both single and multiple pipelines,
using the nodal and loop methods, are presented. Flows in closed conduits are usually driven by
pumps, and the fundamentals of pump performance using dimensional analysis and similitude are
presented. Considerations in selecting a pump include the specific speed under design conditions,
the application of affinity laws in adjusting pump performance curves, the computation of operating
points in pump-pipeline systems, practical limits on pump location based on the critical cavitation
parameter, and the performance of pump systems containing multiple units.
Water-supply systems are designed to meet service-area demands during the design life of the
system. Projection of water demand involves the estimation of per capita demands and population
projections. Over short time scales, populations can be expected to follow either geometric, arith-
metic, or declining growth models, while over longer time scales a logistic growth curve may be
more appropriate. Components of water-supply systems must be designed to accommodate daily
fluctuations in water demand plus potential fire flows. The design periods and capacities of various
components of water-supply systems are listed in Table 2.11. Other key considerations in design-
ing water distribution systems include required service pressures (Table 2.12), pipeline selection
and installation, and provision of adequate storage capacity to meet fire demands and emergency
conditions.
Problems
2.1. Water at 20◦C is flowing in a 100-mm diameter pipe at an average velocity of 2 m/s. If the
diameter of the pipe is suddenly expanded to 150 mm, what is the new velocity in the pipe?
What are the volumetric and mass flowrates in the pipe?

2.2. A 200-mm diameter pipe divides into two smaller pipes each of diameter 100 mm. If the flow
divides equally between the two smaller pipes and the velocity in the 200-mm pipe is 1 m/s,
calculate the velocity and flowrate in each of the smaller pipes.
2.3. The velocity distribution in a pipe is given by the equation
v(r) = Vo

1 −

r
R
2

(2.145)
where v(r) is the velocity at a distance r from the centerline of the pipe, Vo is the centerline
velocity, and R is the radius of the pipe. Calculate the average velocity and flowrate in the
pipe in terms of Vo.
2.4. Calculate the momentum correction coefficient, β, for the velocity distribution given in Equa-
tion 2.145.
2.5. Water is flowing in a horizontal 200-mm diameter pipe at a rate of 0.06 m3/s, and the pressures
at sections 100 m apart are equal to 500 kPa at the upstream section and 400 kPa at the
downstream section. Estimate the average shear stress on the pipe and the friction factor,
f. [Hint: Use Equation 2.26 to calculate the shear stress and Equation 2.32 to calculate the
friction factor.]
2.6. Water at 20◦C flows at a velocity of 2 m/s in a 250-mm diameter horizontal ductile iron pipe.
Estimate the friction factor in the pipe, and state whether the pipe is hydraulically smooth
or rough. Compare the friction factors derived from the Moody diagram, the Colebrook
equation, and the Jain equation. Estimate the change in pressure over 100 m of pipeline.
How would the friction factor and pressure change be affected if the pipe is not horizontal
but 1 m lower at the downstream section?
2.7. Show that the Colebrook equation can be written in the (slightly) more convenient form:
f =
0.25
{log[(ks/D)/3.7 + 2.51/(Re
√
f)]}2
Why is this equation termed “(slightly) more convenient”?
2.8. If you had your choice of estimating the friction factor either from the Moody diagram or
from the Colebrook equation, which one would you pick? Explain your reasons.
2.9. Water leaves a treatment plant in a 500-mm diameter ductile iron pipeline at a pressure of
600 kPa and at a flowrate of 0.50 m3/s. If the elevation of the pipeline at the treatment plant
is 120 m, then estimate the pressure in the pipeline 1 km downstream where the elevation is
100 m. Assess whether the pressure in the pipeline would be sufficient to serve the top floor
of a 10-story (approximately 30 m high) building.
2.10. A 25-mm diameter galvanized iron service pipe is connected to a water main in which the
pressure is 400 kPa. If the length of the service pipe to a faucet is 20 m and the faucet is 2.0
m above the main, estimate the flowrate when the faucet is fully open.

86
2.11. A galvanized iron service pipe from a water main is required to deliver 300 L/s during a fire.
If the length of the service pipe is 40 m and the head loss in the pipe is not to exceed 45 m,
calculate the minimum pipe diameter that can be used. Use the Colebrook equation in your
calculations.
2.12. Repeat Problem 2.11 using the Swamee-Jain equation.
2.13. Use the velocity distribution given in Problem 2.3 to estimate the kinetic energy correction
factor, α, for turbulent pipe flow.
2.14. The velocity profile, v(r), for turbulent flow in smooth pipes is sometimes estimated by the
seventh-root law, originally proposed by Blasius (1911)
v(r) = Vo

1 −
r
R
1
7
where Vo is the maximum (centerline) velocity and R is the radius of the pipe. Estimate the
energy and momentum correction factors corresponding to the seventh-root law.
2.15. Show that the kinetic energy correction factor, α, corresponding to the power-law velocity
profile is given by Equation 2.75. Use this result to confirm your answer to Problem 2.14.
2.16. Water enters and leaves a pump in pipelines of the same diameter and approximately the
same elevation. If the pressure on the inlet side of the pump is 30 kPa and a pressure of
500 kPa is desired for the water leaving the pump, what is the head that must be added by
the pump, and what is the power delivered to the fluid?
2.17. Water leaves a reservoir at 0.06 m3/s through a 200-mm riveted steel pipeline that protrudes
into the reservoir and then immediately turns a 90◦ bend with a minor loss coefficient equal
to 0.3. Estimate the length of pipeline required for the friction losses to account for 90% of
the total losses, which includes both friction losses and so-called “minor losses”. Would it be
fair to say that for pipe lengths shorter than the length calculated in this problem that the
word “minor” should not be used?
2.18. The top floor of an office building is 40 m above street level and is to be supplied with water
from a municipal pipeline buried 1.5 m below street level. The water pressure in the municipal
pipeline is 450 kPa, the sum of the local loss coefficients in the building pipes is 10.0, and the
flow is to be delivered to the top floor at 20 L/s through a 150 mm diameter PVC pipe. The
length of the pipeline in the building is 60 m, the water temperature is 20◦C, and the water
pressure on the top floor must be at least 150 kPa. Will a booster pump be required for the
building? If so, what power must be supplied by the pump?
2.19. Water is pumped from a supply reservoir to a ductile iron water transmission line, as shown
in Figure 2.28. The high point of the transmission line is at point A, 1 km downstream of the
supply reservoir, and the low point of the transmission line is at point B, 1 km downstream
of A. If the flowrate through the pipeline is 1 m3/s, the diameter of the pipe is 750 mm, and
the pressure at A is to be 350 kPa, then: (a) estimate the head that must be added by the
pump; (b) estimate the power supplied by the pump; and (c) calculate the water pressure at
B.

Elev. 7 m
Supply
reservoir
P
Pump
Elev. 10 m
Transmission
line
A
B
Elev. 4 m
Figure 2.28: Problem 2.19
2.20. A pipeline is to be run from a water-treatment plant to a major suburban development 3 km
away. The average daily demand for water at the development is 0.0175 m3/s, and the peak
demand is 0.578 m3/s. Determine the required diameter of ductile iron pipe such that the
flow velocity during peak demand is 2.5 m/s. Round the pipe diameter upward to the nearest
25 mm (i.e., 25 mm, 50 mm, 75 mm, . . . ). The water pressure at the development is to be
at least 340 kPa during average demand conditions, and 140 kPa during peak demand. If the
water at the treatment plant is stored in a ground-level reservoir where the level of the water
is 10.00 m NGVD and the ground elevation at the suburban development is 8.80 m NGVD,
determine the pump power (in kilowatts) that must be available to meet both the average
daily and peak demands.
2.21. Water flows at 5 m3/s in a 1 m × 2 m rectangular concrete pipe. Calculate the head loss over
a length of 100 m.
2.22. Water flows at 10 m3/s in a 2 m × 2 m square reinforced-concrete pipe. If the pipe is laid
on a (downward) slope of 0.002, what is the change in pressure in the pipe over a distance of
500 m?
2.23. Derive the Hazen-Williams head-loss relation, Equation 2.84, starting from Equation 2.82.
2.24. Compare the Hazen-Williams formula for head loss (Equation 2.84) with the Darcy-Weisbach
equation for head loss (Equation 2.33) to determine the expression for the friction factor that
is assumed in the Hazen-Williams formula. Based on your result, identify the type of flow
condition incorporated in the Hazen-Williams formula (rough, smooth, or transition).
2.25. Derive the Manning head-loss relation, Equation 2.86.
2.26. Compare the Manning formula for head loss (Equation 2.86) with the Darcy-Weisbach equa-
tion for head loss (Equation 2.33) to determine the expression for the friction factor that is
assumed in the Manning formula. Based on your result, identify the type of flow condition
incorporated in the Manning formula (rough, smooth, or transition).
2.27. Determine the relationship between the Hazen-Williams roughness coefficient and the Man-
ning roughness coefficient.
2.28. Given a choice between using the Darcy-Weisbach, Hazen-Williams, or Manning equations to
estimate the friction losses in a pipeline, which equation would you choose? Why?

88
2.29. Water flows at a velocity of 2 m/s in a 300-mm new ductile iron pipe. Estimate the head
loss over 500 m using: (a) the Hazen-Williams formula; (b) the Manning formula; and (c) the
Darcy-Weisbach equation. Compare your results. Calculate the Hazen-Williams roughness
coefficient and the Manning coefficient that should be used to obtain the same head loss as
the Darcy-Weisbach equation.
2.30. Reservoirs A, B, and C are connected as shown in Figure 2.29. The water elevations in
reservoirs A, B, and C are 100 m, 80 m, and 60 m, respectively. The three pipes connecting
the reservoirs meet at the junction J, with pipe AJ being 900 m long, BJ 800 m long, CJ
700 m long, and the diameter of all pipes equal to 850 mm. If all pipes are made of ductile
iron and the water temperature is 20◦C, find the flow into or out of each reservoir.
Elev.
100 m
A Elev.
80 m
B
Elev.
60 m
C
LAJ 5 900 m
LBJ 5 800 m
LJC 5 700 m
J
2.31. The water-supply network shown in Figure 2.30 has constant-head elevated storage tanks at
A and B, with inflows and withdrawals at C and D. The network is on flat terrain, and the
pipeline characteristics are as follows:
0.2 m3/s
Reservoir
Elev. 25 m
0.2 m3/s
Reservoir
Elev. 20 m
A C
D B
L D
Pipe (km) (mm)
AD 1.0 400
BC 0.8 300
BD 1.2 350
AC 0.7 250
If all pipes are made of ductile iron, calculate the inflows/outflows from the storage tanks.
Assume that the flows in all pipes are fully turbulent.
2.32. Consider the pipe network shown in Figure 2.31. The Hardy Cross method can be used to
calculate the pressure distribution in the system, where the friction loss, hf , is estimated

using the equation
hf = rQn
and all pipes are made of ductile iron. What value of r and n would you use for each pipe in
the system? The pipeline characteristics are as follows:
L D
Pipe (m) (mm)
AB 1,000 300
BC 750 325
CD 800 200
DE 700 250
EF 900 300
FA 900 250
BE 950 350
You can assume that the flow in each pipe is hydraulically rough.
A C
0.5 m3/s
0.5 m3/s
F D
B
E
2.33. A portion of a municipal water distribution network is shown in Figure 2.32, where all pipes
are made of ductile iron and have diameters of 300 mm. Use the Hardy Cross method to find
the flowrate in each pipe. If the pressure at point P is 500 kPa and the distribution network
is on flat terrain, determine the water pressures at each pipe intersection.
150 m 150 m
100 m
100 m
100 m
100 m
0.1 m3/s
0.07 m3/s
0.06 m3/s
0.05 m3/s
0.06 m3/s
150 m 150 m
150 m 150 m
P
2.34. What is the constant that can be used to convert the specific speed in SI units (Equation
2.111) to the specific speed in U.S. Customary units (Equation 2.112)?
2.35. What is the highest synchronous speed for a motor driving a pump?

90
2.36. Derive the affinity relationship for the power delivered to a fluid by two homologous pumps.
[Note: This affinity relation is given by Equation 2.116.]
2.37. A pump is required to deliver 150 L/s (± 10%) through a 300-mm diameter PVC pipe from
a well to a reservoir. The water level in the well is 1.5 m below the ground and the water
surface in the reservoir is 2 m above the ground. The delivery pipe is 300 m long, and minor
losses can be neglected. A pump manufacturer suggests using a pump with a performance
curve given by
hp = 6 − 6.67 × 10−5
Q2
where hp is in meters and Q in L/s. Is this pump adequate?
2.38. A pump is to be selected to deliver water from a well to a treatment plant through a 300-
m long pipeline. The temperature of the water is 20◦C, the average elevation of the water
surface in the well is 5 m below ground surface, the pump is 50 cm above ground surface, and
the water surface in the receiving reservoir at the water-treatment plant is 4 m above ground
surface. The delivery pipe is made of ductile iron (ks = 0.26 mm) with a diameter of 800
mm. If the selected pump has a performance curve of hp = 12 − 0.1Q2, where Q is in m3/s
and hp is in m, then what is the flowrate through the system? Calculate the specific speed of
the required pump (in U.S. Customary units), and state what type of pump will be required
when the speed of the pump motor is 1,200 rpm. Neglect minor losses.
2.39. A pump lifts water through a 100-mm diameter ductile iron pipe from a lower to an upper
reservoir (Figure 2.33). If the difference in elevation between the reservoir surfaces is 10 m,
and the performance curve of the 2400-rpm pump is given by
hp = 15 − 0.1Q2
where hp is in meters and Q in L/s, then estimate the flowrate through the system. If
the pump manufacturer gives the required net positive suction head under these operating
conditions as 1.5 m, what is the maximum height above the lower reservoir that the pump
can be placed and maintain the same operating conditions?
10 m
100 m
Lower
reservoir
1 m
Upper
reservoir
P
3 m

2.40. Water is being pumped from reservoir A to reservoir F through a 30-m long PVC pipe of
diameter 150 mm (see Figure 2.34). There is an open gate valve located at C; 90◦ bends
(threaded) located at B, D, and E; and the pump performance curve is given by
hp = 20 − 4713Q2
where hp is the head added by the pump in meters and Q is the flowrate in m3/s. The
specific speed of the pump (in U.S. Customary units) is 3,000. Assuming that the flow is
turbulent (in the smooth, rough, or transition range) and the temperature of the water is
20◦C, then (a) write the energy equation between the upper and lower reservoirs, accounting
for entrance, exit, and minor losses between A and F; (b) calculate the flowrate and velocity
in the pipe; (c) if the required net positive suction head at the pump operating point is 3.0
m, assess the potential for cavitation in the pump (for this analysis you may assume that the
head loss in the pipe is negligible between the intake and the pump); and (d) use the affinity
laws to estimate the pump performance curve when the motor on the pump is changed from
800 rpm to 1,600 rpm.
P
3 m
F
E
A
B C
D
10 m
2.41. If the performance curve of a certain pump model is given by
hp = 30 − 0.05Q2
where hp is in meters and Q is in L/s, what is the performance curve of a pump system
containing n of these pumps in series? What is the performance curve of a pump system
containing n of these pumps in parallel?
2.42. A pump is placed in a pipe system in which the energy equation (system curve) is given by
hp = 15 + 0.03Q2
where hp is the head added by the pump in meters and Q is the flowrate through the system
in L/s. The performance curve of the pump is
hp = 20 − 0.08Q2
What is the flowrate through the system? If the pump is replaced by two identical pumps in
parallel, what would be the flowrate in the system? If the pump is replaced by two identical
pumps in series, what would be the flowrate in the system?

92
2.43. Derive an expression for the population, P, versus time, t, where the growth rate is: (a)
geometric, (b) arithmetic, and (c) declining.
2.44. The design life of a planned water-distribution system is to end in the year 2030, and the
population in the town has been measured every 10 years since 1920 by the U.S. Census
Bureau. The reported populations are tabulated below. Estimate the population in the
town using: (a) graphical extension, (b) arithmetic growth projection, (c) geometric growth
projection, (d) declining growth projection (assuming a saturation concentration of 100,000
people), and (e) logistic curve projection.
Year Population
1920 25,521
1930 30,208
1940 30,721
1950 37,253
1960 38,302
1970 41,983
1980 56,451
1990 64,109
2.45. A city founded in 1950 had a population of 13,000 in 1960; 125,000 in 1975; and 300,000 in
1990. Assuming that the population growth follows a logistic curve, estimate the saturation
population of the city.
2.46. The average demand of a population served by a water-distribution system is 580 L/d/capita,
and the population at the end of the design life is estimated to be 100,000 people. Estimate
the maximum daily demand and maximum hourly demand.
2.47. Estimate the flowrate and volume of water required to provide adequate fire protection to
a five-story office building constructed of joisted masonry. The effective floor area of the
building is 5,000 m2.
2.48. What is the maximum fire flow and corresponding duration that can be estimated for any
building?
2.49. A water-supply system is being designed to serve a population of 200,000 people, with an
average per capita demand of 600 L/d/person and a needed fire flow of 28,000 L/min. If the
water supply is to be drawn from a river, then what should be the design capacity of the
supply pumps and water-treatment plant? For what duration must the fire flow be sustained,
and what volume of water must be kept in the service reservoir to accommodate a fire? What
should the design capacity of the distribution pipes be?
2.50. What is the minimum acceptable water pressure in a distribution system under average daily
demand conditions?
2.51. Calculate the volume of storage required for the elevated storage reservoir in the water-supply
system described in Problem 2.49.

Bibliography
[1] M. Abramowitz and I.A. Stegun. Handbook of Mathematical Functions. Dover, New York,
New York, 1965.
[2] M. Abramowitz and I.A. Stegun. Handbook of Mathematical Functions. Dover, New York,
New York, 1972.
[3] W. Abtew. Evapotranspiration Measurements and Modeling for Three Wetland Systems in
South Florida. Journal of the American Water Resources Association, 32(3):465–473, 1996.
[4] W. Abtew, J.Obeysekera, M. Irizarry-Ortiz, D. Lyons, and A. Reardon. Evapotranspiration
Estimation for South Florida. EMA 407, South Florida Water Management District, West
Palm Beach, Florida, January 2003.
[5] W. Abtew and J. Obeysekera. Lysimeter study of evapotranspiration of cattails and com-
parison of three estimation methods. Transactions of the American Society of Agricultural
Engineers, 38(1):121–129, 1995.
[6] M.M. Abu-Seida and A.A. Quraishi. A ﬂow equation for submerged rectangular weirs. Pro-
ceedings of the Institution of Civil Engineers, 61(2):685–696, 1976.
[7] P. Ackers, W.R. White, J.A. Perkins, and A.J.M. Harrison. Weirs and Flumes for Flow
Measurement. Wiley, Chichester, 1978.
[8] N. Ahmed and D.K. Sunada. Nonlinear ﬂow in porous media. Journal of the Hydraulics
Division, ASCE, 95(HY6):1847–1857, 1969.
[9] T.P. Ahrens. Well design criteria. Water Well Journal, National Water Well Association,
September and November 1957.
[10] A.J. Aisenbrey, Jr., R.B. Hayes, H.J. Warren, D.L. Winsett, and R.B. Young. Design of
Small Canal Structures. United States Department of the Interior, Bureau of Reclamation,
Denver, Colorado, 1974.
[11] A.O. Akan. Urban Stormwater Hydrology. Technomic Publishing Company, Inc., Lancaster,
Pennsylvania, 1993.
[12] R. Aldridge and R.J. Jackson. Interception of rainfall by hard beech. New Zealand Journal
of Science, 16:185–198, 1973.
805

806
[13] A. Alexandrou. Principles of Fluid Mechanics. Prentice-Hall, Upper Saddle River, New
Jersey, 2001.
[14] Y. Alila. Regional rainfall depth-duration-frequency equations for Canada. Water Resources
Research, 36(7):1767–1778, July 2000.
[15] R.G. Allen. A Penman for all seasons. Journal of Irrigation and Drainage Engineering,
ASCE, 112(4):348–368, 1986.
[16] R.G. Allen. Self-calibrating method for estimating solar radiation from air temperature.
Journal of Irrigation and Drainage Engineering, ASCE, 2(2):56–67, April 1997.
[17] R.G. Allen, M.E. Jensen, J.L. Wright, and R.D. Burman. Operational estimates of reference
evapotranspiration. Journal of Agronomy, 81:650–662, 1989.
[18] R.G. Allen, L.S. Pereira, D. Raes, and M. Smith. Crop evapotranspiration. Guidelines for
computer crop water requirements. Irrigation and Drainage Paper 56, Food and Agricultural
Organization of the United Nations (FAO), Rome, Italy, 1998.
[19] R.G. Allen and W.O. Pruitt. Rational use of the FAO Blaney-Criddle formula. Journal of
Irrigation and Drainage Engineering, ASCE, 112(IR2):139–155, 1986.
[20] R.G. Allen, M. Smith, L.S. Pereira, and A. Perrier. An update for the calculation of reference
evapotranspiration. ICID Bulletin, 43(2):35–92, 1994b.
[21] R.G. Allen, M. Smith, A. Perrier, and L.S. Pereira. An update for the definition of reference
evapotranspiration. ICID Bulletin, 43(2):1–34, 1994a.
[22] M. Amein. Stream flow routing on computer by characteristics. Water Resources Research,
2(1):123–130, 1966.
[23] M. Amein and C.S. Fang. Stream flow routing (with applications to North Carolina rivers).
Report 17, Water Resources Research Institute of the University of North Carolina, Raleigh,
North Carolina, 1969.
[24] American Concrete Pipe Association. Concrete Pipe Handbook. American Concrete Pipe
Association, Vienna, Virginia, 1981.
[25] American Concrete Pipe Association. Concrete Pipe Design Manual. American Concrete
Pipe Association, Vienna, Virginia, 1985.
[26] American Iron and Steel Institute. Modern Sewer Design. AISI, Washington, DC, third
edition, 1995.
[27] American Society for Testing and Materials. Standard practice for design and installation of
ground water monitoring wells in aquifers. Technical Report D 5092-1990, ASTM Committee
D-18 on Soil and Rock, 1990.
[28] American Society for Testing and Materials. Standard guide for selection of aquifer test
method in determining of hydraulic properties by well techniques. Technical Report D 4043-
91, ASTM Committee D-18 on Soil and Rock, 1991a.

[29] American Society for Testing and Materials. Standard test method (field procedure) for
withdrawal and injection well tests for determining hydraulic properties of aquifer systems.
Technical Report D 4050-91, ASTM Committee D-18 on Soil and Rock, 1991b.
[30] American Society for Testing and Materials. Standard test method (analytical procedure)
for determining transmissivity and storage coefficient of nonleaky confined aquifers by over-
damped well response to instantaneous change in head(slug test). Technical Report D 4106-91,
ASTM Committee D-18 on Soil and Rock, 1991c.
[31] American Society of Civil Engineers. Report of ASCE Task Force on Friction Factors in Open
Channels. Proceedings of the American Society of Civil Engineers, 89(HY2):97, March 1963.
[32] American Society of Civil Engineers. Gravity Sanitary Sewer Design and Construction. Amer-
ican Society of Civil Engineers, New York, New York, 1982. Manual of Practice No.60.
[33] American Society of Civil Engineers. Civil engineering guidelines for planning and designing
hydroelectric developments. ASCE, New York, New York, 1989.
[34] American Society of Civil Engineers. Design and Construction of Urban Stormwater Man-
agement Systems. American Society of Civil Engineers, New York, New York, 1992.
[35] American Society of Civil Engineers. Hydrology Handbook. American Society of Civil Engi-
neers, New York, New York, second edition, 1996. Manual of Practice No.28.
[36] American Society of Civil Engineers. Technical Engineering and Design Guides as Adapted
from the US Army Corps of Engineers, No.19: Flood-Runoff Analysis. ASCE Press, New
York, New York, 1996.
[37] American Society of Civil Engineers. Urban Runoff Quality Management. American Society
of Civil Engineers, New York, New York, 1998. Manual of Practice No.23.
[38] American Society of Heating, Refrigerating and Air Conditioning Engineers. ASHRAE Hand-
book, 1981. Fundamentals. ASHRAE, New York, New York, 1981.
[39] American Water Works Association. 1984 Water Utility Operating Data. AWWA, Denver,
Colorado, 1986.
[40] American Water Works Association. Distribution System Requirements for Fire Protection,
Manual of Water Supply Practices M31. AWWA, Denver, Colorado, 1992.
[41] American Water Works Association. Water Resources Planning, Manual of Water Supply
Practices M50. AWWA, Denver, Colorado, First edition, 2001.
[42] American Water Works Association. PVC Pipe–Design and Installation, Manual of Water
Supply Practices M23. AWWA, Denver, Colorado, Second edition, 2002b.
[43] American Water Works Association. Water Sources. Principles and Practices of Water Supply
Operations. AWWA, Denver, Colorado, Third edition, 2003a.
[44] American Water Works Association. Groundwater, Manual of Water Supply Practices M21.
AWWA, Denver, Colorado, Third edition, 2003b.

808
[45] American Water Works Association. Water Transmission and Distribution. AWWA, Denver,
Colorado, Third edition, 2003c.
[46] American Water Works Association. Ductile-Iron Pipe and Fittings, Manual of Water Supply
Practices M41. AWWA, Denver, Colorado, Second edition, 2003d.
[47] American Water Works Association. Sizing Water Service Lines and Meters, Manual of
Water Supply Practices M22. AWWA, Denver, Colorado, Second edition, 2004.
[48] American Water Works Association. American National Standard for Polyethylene Encase-
ment for Ductile-Iron Pipe Systems. ANSI/AWWA C105/A21.5. AWWA, Denver, Colorado,
latest edition.
[49] American Water Works Association. AWWA Standard for Cement-Mortar Protective Lining
and Coating for Steel Water Pipe–4 in. (100 mm) and Larger–Shop Applied. ANSI/AWWA
C205. AWWA, Denver, Colorado, latest edition.
[50] American Water Works Association. AWWA Standard for Concrete Pressure Pipe, Bar-
Wrapped, Steel Cylinder Type. ANSI/AWWA C303. AWWA, Denver, Colorado, latest edition.
[51] American Water Works Association. AWWA Standard for Design of Prestressed Concrete
Cylinder Pipe. ANSI/AWWA C304. AWWA, Denver, Colorado, latest edition.
[52] American Water Works Association. AWWA Standard for Fiberglass Pressure Pipe.
ANSI/AWWA C950. AWWA, Denver, Colorado, latest edition.
[53] American Water Works Association. AWWA Standard for Liquid-Epoxy Coating Systems for
the Interior and Exterior of Steel Water Pipelines. ANSI/AWWA C210. AWWA, Denver,
Colorado, latest edition.
[54] American Water Works Association. AWWA Standard for Polyethylene (PE) Pressure Pipe
and Fittings, 4 in. (100 mm) through 63 in. (1575 mm) for Water Distribution and Trans-
mission. ANSI/AWWA C906. AWWA, Denver, Colorado, latest edition.
[55] American Water Works Association. AWWA Standard for Prestressed Concrete Pressure
Pipe, Steel Cylinder Type. ANSI/AWWA C301. AWWA, Denver, Colorado, latest edition.
[56] American Water Works Association. AWWA Standard for Reinforced Concrete Pressure Pipe,
Steel-Cylinder Type. ANSI/AWWA C300. AWWA, Denver, Colorado, latest edition.
[57] American Water Works Association. Manual M11, Steel Pipe–A Guide for Design and In-
stallation. AWWA, Denver, Colorado, latest edition.
[58] American Water Works Association. Manual M9, Concrete Pressure Pipe. AWWA, Denver,
Colorado, latest edition.
[59] W.F. Ames. Numerical Methods for Partial Diﬀerential Equations. Academic Press, New
York, New York, second edition, 1977.

[60] A.G. Anderson, A.. Painta, and J.T. Davenport. Tentative design procedure for riprap lined
channels. Technical report, Highway Research Board, National Academy of Sciences, Wash-
ington, DC, 1970. NCHRP Report No. 108.
[61] M.G. Anderson and T.P. Burt. The role of topography in controlling throughflow generation.
Earth Surface Processes and Landforms, 3:27–36, 1978.
[62] M.P. Anderson and W.W. Woessner. Applied Groundwater Modeling, Simulation of Flow and
Transport. Academic Press, New York, New York, 1992.
[63] ASCE. Elevated water tank rises to new levels. Civil Engineering, 70(1):19, January 2000.
[64] ASCE Task Committee on Ground Water Protection. Ground Water, Protection Alternatives
and Strategies in the U.S.A. ASCE, New York, 1997.
[65] ASME B36.19M. Stainless Steel Pipe. American Society of Mechanical Engineers, New York,
New York, 1985.
[66] Atlanta Regional Commission/Georgia Department of Natural Resources-Environmental
Protection Division, Atlanta, Georgia. Georgia Stormwater Management Manual, 2003.
www.georgiastormwater.com.
[67] G. Aussenac and C. Boulangeat. Interception des precipitation et evapotranspiration reelle
dans des peuplements de feuillu (fagus silvatica L.) et de resineux (pseudotsuga menziesii
(Mirb.) Franco). Annales des Sciences Forestieres, 37(2):91–107, 1980.
[68] H.E. Babbitt and E.R. Baumann. Sewerage and Sewage Treatment. John Wiley Sons, New
[69] W. Badon-Ghyben. Nota in Verband met de Voorgenomen Putboring Nabij Amsterdam
(Notes on the probable results of well drilling near Amsterdam). Technical Report 1888/9,
Tijdschr. Kon. Inst. Ing., The Hague, 1888.
[70] B.A. Bakhmeteff. Hydraulics of Open Channel Flow. McGraw-Hill, Inc., New York, New
York, 1932.
[71] Barre de Saint-Venant. Theory of unsteady water flow, with application to river floods and
to propagation of tides in river channels. French Academy of Science, 73:148–154, 237–240,
1871.
[72] V. Batu. Aquifer Hydraulics. John Wiley Sons, New York, New York, 1998.
[73] J. Bear. Dynamics of Fluids in Porous Media. Dover Publications, Inc., New York, New
York, 1972.
[74] J. Bear. Hydraulics of Groundwater. McGraw-Hill Book Company, New York, New York,
1979.
[75] J. Bear and G. Dagan. The transition zone between fresh and salt waters in a coastal aquifer,
Progress Report 1:The steady interface between two immiscible fluids in a two-dimensional
field of flow. Technical report, Hydraulic Lab, Technion, Haifa, Israel, 1962.

810
[76] J.S. Beard. Rainfall interception by grass. South African Forestry Journal, 42:12–25, 1962.
[77] P.B. Bedient and W.C. Huber. Hydrology and Floodplain Analysis. Prentice-Hall, Upper
Saddle River, New Jersey, 1992.
[78] P.B. Bedient and W.C. Huber. Hydrology and Floodplain Analysis. Prentice-Hall, Upper
Saddle River, New Jersey, third edition, 2002.
[79] P.B. Bedient, H.S. Rifai, and C.J. Newell. Ground Water Contamination. Prentice-Hall,
Upper Saddle River, New Jersey, second edition, 1999.
[80] T.V. Belanger and M.T. Montgomery. Seepage meter errors. Limnol. Oceanogr., 37:1787–
1795, 1992.
[81] J.R. Benjamin and C. Allin Cornell. Probability, Statistics, and Decision for Civil Engineers.
McGraw-Hill, Inc., New York, New York, 1970.
[82] R.P. Betson. What is watershed runoff? Journal of Geophysical Research, 69(8):1541–1552,
1964.
[83] W.R. Bidlake, W.M. Woodham, and M.A. Lopez. Evapotranspiration from Areas of Native
Vegetation in West-Central Florida. Water-Supply Paper 2430, U.S. Geological Survey, 1996.
[84] R.B. Billings and C.V. Jones. Forecasting Urban Water Demand. American Water Works
Association, Denver, Colorado, 1996.
[85] J.H. Black and K.L. Kipp. Observation well response time and its effect upon aquifer test
results. Journal of Hydrology, 34:297–306, 1977.
[86] P.E. Black. Watershed Hydrology. Ann Arbor Press, Inc., Chelsea, Michigan, second edition,
1996.
[87] H. Blasius. Das Ähnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten. Forsch. Gebiete
Ingenieurw., 131, 1913.
[88] R.D. Blevins. Applied Fluid Dynamics Handbook. Van Nostrand Reinhold, New York, New
York, 1984.
[89] F.E. Blow. Quantity and hydrologic characteristics of litter upon upland oak forests in eastern
Tennessee. Journal of Forestry, 53:190–195, 1955.
[90] B.B. Bobée and R. Robitaille. Correction of bias in estimation of the coefficient of skewness.
Water Resources Research, 11(6):851–854, December 1975.
[91] G.L. Bodhaine. Measurement of Peak Discharge at Culverts by Indirect Methods. Techniques
of Water Resources Investigations Chapter A3, Book 3, U.S. Geological Survey, Washington,
DC, 1976.
[92] G.H. Bolt and P.H. Groenvelt. Coupling phenomena as a possible cause for non-darcian
behavior of water in soil. Bull. Intern. Assoc. Sci. Hydrol., 14:17–26, 1969.

[93] F.A. Bombardelli and M.H. Garcı́a. Hydraulic design of Large-Diameter Pipes. Journal of
Hydraulic Engineering, 129(11):839–846, November 2003.
[94] J. Boonstra. Well hydraulics and aquifer tests. In J.W. Delleur, editor, The Handbook of
Groundwater Engineering, pages 8.1–8.34. CRC Press, Inc., Boca Raton, Florida, 1998a.
[95] L.E. Borgman. Risk criteria. Journal of Waterways and Harbors Division, ASCE,
89(WW3):1–35, August 1963.
[96] M.G. Bos. Discharge Measurement Structures. Wageningen, the Netherlands, third revised
edition, 1988. ILRI Publication 20.
[97] Boulder County. Drainage Criteria Manual. Boulder County, Colorado, 1984.
[98] D. Bousmar and Y. Zech. Momentum transfer for practical flow computation in compound
channels. Journal of Water Resources Planning and Management, 125(7):696–706, July 1999.
[99] H. Bouwer. Groundwater Hydrology. McGraw-Hill Book Company, New York, New York,
1978.
[100] H. Bouwer. Elements of soil science and groundwater hydrology. In G. Bitton and C.P. Gerba,
editors, Groundwater Pollution Microbiology, pages 9–38. Krieger Publishing Company, Mal-
abar, Florida, 1984.
[101] H. Bouwer. The Bouwer and Rice slug test: An update. Ground Water, 27:304–309, 1989.
[102] H. Bouwer. Discussion of Bouwer and Rice slug test review articles. Ground Water, 34:171,
1996.
[103] H. Bouwer, J.T. Back, and J.M. Oliver. Predicting infiltration and ground-water mounds for
artificial recharge. Journal of Hydrologic Engineering, 4(4):350–357, 1999.
[104] H. Bouwer and R.C. Rice. A slug test for determining hydraulic conductivity of unconfined
aquifers with completely or partially penetrating wells. Water Resources Research, 12:423–
428, 1976.
[105] N.C. Brady. The Nature and Properties of Soils. Macmillan, New York, 8th edition, 1974.
[106] E.F. Brater, H.W. King, J.E. Lindell, and C.Y. Wei. Handbook of Hydraulics. McGraw-Hill,
Inc., New York, New York, seventh edition, 1996.
[107] W.C. Bridges. Techniques for estimating magnitude and frequency of floods on natural-flow
streams in Florida. Water-Resources Investigations Report 82-4012, United States Geological
Survey, Reston, Virginia, 1982.
[108] J. Bromley, M. Robinson, and J.A. Barker. Scale-dependency of hydraulic conductivity: an
example from Thorne Moor, a raised mire in South Yorkshire, UK. Hydrological Processes,
18:973–985, 2004.
[109] K.N. Brooks, P.F. Folliott, H.M. Gregersen, and J.L. Thames. Hydrology and the Management
of Watersheds. Iowa State University Press, Ames, Iowa, 1991.

812
[110] D.S. Brookshire and D. Whittington. Water resources issues in developing countries. Water
Resources Research, 29(7):1883–1888, July 1993.
[111] G.O. Brown. Henry Darcy and the making of a law. Water Resources Research, 38(7),
doi:10.1029/2001WR000727, 2002.
[112] G.M. Brune. Trap Efficiency of Reservoirs. Transactions of the American Geophysical Union,
34(3):407–418, 1953.
[113] D. Brunt. Notes on radiation in the atmosphere. Quarterly Journal of Royal Meteorological
Society, 58:389–418, 1932.
[114] W. Brutsaert. Evaporation into the Atmosphere: Theory, History, and Applications. R.
Deidel, Dordrecht, The Netherlands, 1982.
[115] P.H. Burgi. Bicycle-Safe Grate Inlets Study: Volume 2–Hydraulic Characteristics of Three
Selected Grate Inlets on Continuous Grades. Technical Report FHWA-RD-78-4, Federal
Highway Administration, U.S. Department of Transportation, Washington, DC, 1978.
[116] F.L. Burton. Wastewater-Collection Systems. In L.W. Mays, editor, Water Resources Hand-
book, pages 19.1–19.53. McGraw-Hill, Inc., New York, New York, 1996.
[117] K. Bury. Statistical Distributions in Engineering. Cambridge University Press, New York,
New York, 1999.
[118] J.A. Businger. Some remarks on Penman’s equations for the evapotranspiration. Netherlands
J. Agric. Sci., 4:77, 1956.
[119] D. Butler and J.W. Davies. Urban Drainage. E FN Spon, London, England, 2000.
[120] J.J. Butler Jr., C.D. McElwee, and W. Liu. Improving the quality of parameter estimates
obtained from slug tests. Ground Water, 34(3):480–490, 1996.
[121] T.R. Camp. Design of sewers to facilitate flow. Sewer Works Journal, 18:3, 1946.
[122] G.S. Campbell. An Introduction to Environmental Physics. Springer, New York, 1977.
[123] M.D. Campbell and J.H. Lehr. Water Well Technology. McGraw-Hill Book Company, Inc.,
New York, New York, 1972.
[124] P.C. Carman. Fluid flow through a granular bed. Transaction of the Institutions of Chemical
Engineers, 15:150–156, 1937.
[125] P.C. Carman. Flow of Gasses Through Porous Media. Butterworths, London, Great Britain,
1956.
[126] D. Carroll. Rainwater as a chemical agent and geologic processes- A review. Water-Supply
Paper 1535-G, United States Geological Survey, 1962.
[127] H.W. Carslaw and J.C. Jaeger. Conduction of Heat in Solids. Oxford University Press, New
York, New York, second edition, 1959.

[128] T.V. Cech. Principles of Water Resources. John Wiley Sons, New York, New York, 2002.
[129] H.R. Cedergren, K.H. O’Brien, and J.A. Arman. Guidelines for the design of subsurface
drainage systems for highway structural sections. Technical Report FHWA-RD-72-30, Federal
Highway Administration, June 1972.
[130] A. Chadwick and J. Morfett. Hydraulics in Civil and Environmental Engineering. E FN
Spon, London, England, second edition, 1993.
[131] R.A. Chandler and D.B. McWhorter. Upconing of the salt-water–fresh-water interface be-
neath a pumping well. Ground Water, 13:354–359, 1975.
[132] M. Chang. Forest Hydrology: An Introduction to Water and Forests. CRC Press, Inc., Boca
Raton, Florida, 2002.
[133] R.J. Charbeneau. Groundwater Hydraulics and Pollutant Transport. Prentice-Hall, Upper
Saddle River, New Jersey, 2000.
[134] D.V. Chase. Operation of water distribution systems. In L.W. Mays, editor, Water Distri-
bution Systems Handbook, pages 15.1–15.16. McGraw-Hill Book Company, New York, New
York, 2000.
[135] M.H. Chaudhry. Open-Channel Flow. Prentice-Hall, Upper Saddle River, New Jersey, 1993.
[136] C. Chen. Rainfall intensity-duration-frequency formulas. Journal of Hydraulic Engineering,
109(12):1603–1621, 1983.
[137] C.-N. Chen and T.S.W. Wong. Critical rainfall duration for maximum discharge from overland
plane. Journal of Hydraulic Engineering, 119(9):1040–1045, September 1993.
[138] A.H.-D. Cheng. Multilayered Aquifer Systems: Fundamentals and Applications. Marcel
Dekker, Inc., New York, New York, 2000.
[139] D.A. Chin. Leakage of clogged channels that partially penetrate surﬁcial aquifers. Journal
of Hydraulic Engineering, 117(4):467–488, April 1991.
[140] D.A. Chin. Analysis and Prediction of South-Florida Rainfall. Technical Report CEN-93-2,
University of Miami, Coral Gables, Florida, 1993.
[141] D.A. Chin. A risk management strategy for wellhead protection. Technical Report CEN93-3,
University of Miami, Department of Civil Engineering, Coral Gables, Florida, 1993.
[142] D.A. Chin and P.V.K. Chittaluru. Risk management in wellhead protection. Journal of
Water Resources Planning and Management, 120(3):294–315, 1994.
[143] C.-L. Chiu and N.-C. Tung. Maximum Velocity and Regularities in Open-Channel Flow.
Journal of Hydraulic Engineering, 128(4):390–398, April 2002.
[144] V.T. Chow. Frequency analysis of hydrologic data with special application to rainfall inten-
sities. Bulletin 414, University of Illinois Engineering Experiment Station, 1953.

814
[145] V.T. Chow. The log-probability law and its emerging applications. Proceedings of the Amer-
ican Society of Civil Engineers, 80:536–1 to 536–25, 1954.
[146] V.T. Chow. Open-Channel Hydraulics. McGraw-Hill, Inc., New York, New York, 1959.
[147] V.T. Chow. Handbook of Applied Hydrology. McGraw-Hill, Inc., New York, New York, 1964.
[148] V.T. Chow, D.R. Maidment, and L.W. Mays. Applied Hydrology. McGraw-Hill, Inc., New
[149] J.E. Christiansen. Pan evaporation and evapotranspiration from climatic data. Journal of
Irrigation and Drainage Engineering, ASCE, 94:243–265, 1968.
[150] J.E. Christiansen and G.H. Hargreaves. Irrigation requirements from evaporation. Trans.
Int. Comm. on Irrig. and Drain., III:23.569–23.596, 1969.
[151] C.O. Clark. Storage and the Unit Hydrograph. Transactions of the American Society of Civil
Engineers, 110:1419–1446, 1945.
[152] R.M. Clark. Water Supply. In R.A. Corbitt, editor, Standard Handbook of Environmental
Engineering, pages 5.1–5.225. McGraw-Hill, Inc., New York, New York, 1990.
[153] C.F. Colebrook. Turbulent Flow in Pipes, with Particular Reference to the Transition Region
Between the Smooth and Rough Pipe Laws. Journal, Institution of Civil Engineers (London),
11:133–156, February 1939.
[154] H.H. Cooper, J.D. Bredehoeft, and I.S. Papadopulos. Response of a ﬁnite-diameter well to
an instantaneous charge of water. Water Resources Research, 3(1):263–269, 1967.
[155] H.H. Cooper and C.E. Jacob. A generalized graphical method for evaluating formation
constants and summarizing well-ﬁeld history. Transactions of the American Geophysical
Union, 27:526–534, 1946.
[156] R.A. Corbitt. Wastewater Disposal. In R.A. Corbitt, editor, Standard Handbook of Environ-
mental Engineering, pages 6.1–6.274. McGraw-Hill, Inc., New York, New York, 1990.
[157] G.K. Cotton. Hydraulic Design of Flood Control Channels. In L.W. Mays, editor, Stormwater
Collection Systems Design Handbook, pages 16.1–16.42. McGraw-Hill, Inc., New York, New
York, 2001.
[158] N.H. Crawford and R.K. Linsley. Digital Simulation in Hydrology, Stanford Watershed Model
IV. Technical Report 39, Department of Civil Engineering, Stanford University, Stanford,
California, 1966.
[159] H. Cross. Analysis of Flow in Networks of Conduits or Conductors. Bulletin 286, University
of Illinois Engineering Experiment Station, 1936.
[160] Z. Şen. Applied Hydrogeology for Scientists and Engineers. Lewis Publishers, Boca Raton,
Florida, 1995.

[161] J.A. Cunge. On the subject of a flood propagation computation method (Muskingum
method). Journal of Hydraulic Research, IAHR, 7(2):205–230, 1969.
[162] C. Cunnane. Methods and merits of regional flood frequency analysis. Journal of Hydrology,
100:269–290, 1988.
[163] G. Dagan. Flow and Transport in Porous Formations. Springer-Verlag, New York, New York,
1989.
[164] M. Dagg. Evaporation Pans in East Africa, 1968. Proceedings Fourth Specialist Meeting on
Applied Meteorology in East Africa.
[165] J.W. Daily and D.R.F. Harleman. Fluid Dynamics. Addison-Wesley Publishing Company,
Inc., Reading, Massachusetts, 1966.
[166] H. Darcy. Les Fontaines Publiques de la Ville de Dijon. Victor Dalmont, Paris, France, 1856.
[167] T. Davie. Fundamentals of Hydrology. Routledge, London, England, 2002.
[168] G. de Marsily. Quantitative Hydrogeology, Groundwater Hydrology for Engineers. Academic
Press, Inc., San Diego, California, 1986.
[169] T.N. Debo and A.J. Reese. Municipal Storm Water Management. Lewis Publishers, Inc.,
Boca Raton, Florida, 1995.
[170] G.J. DeGlee. Over Grondwaterstromingen bij Wateronttrekking Door Middel van Putten (in
Dutch). J. Waltman, Delft, 1930.
[171] J. Delleur. The Evolution of Urban Hydrology: Past, Present, and Future. Journal of
Hydraulic Engineering, 129(8):563–573, August 2003.
[172] J.L. Devore. Probability and Statistics for Engineering and the Sciences. Brooks/Cole, Pacific
Grove, California, 2000.
[173] S.L. Dingman. Fluvial Hydrology. W.H. Freeman and Company, New York, New York, 1984.
[174] S.L. Dingman. Physical Hydrology. Prentice-Hall, Upper Saddle River, New Jersey, second
edition, 2002.
[175] R.D. Dodson. Storm Water Pollution Control. McGraw-Hill, Inc., New York, New York,
second edition, 1998.
[176] R.D. Dodson. Floodplain hydraulics. In L.W. Mays, editor, Hydraulic Design Handbook,
pages 19.1–19.50. McGraw-Hill Book Company, New York, New York, 1999.
[177] R.D. Dodson and C.T. Maske. Regulation of Stormwater Collection Systems in the United
States. In L.W. Mays, editor, Stormwater Collection Systems Design Handbook, pages 2.1–
2.25. McGraw-Hill, Inc., New York, New York, 2001.
[178] P.A. Domenico and M.D. Mifflin. Water from low-permeability sediments and land subsidence.
Water Resources Research, 1:563–576, 1965.

816
[179] P.A. Domenico and F.W. Schwartz. Physical and Chemical Hydrogeology. John Wiley
Sons, New York, New York, second edition, 1998.
[180] J. Doorenbos and W.O. Pruitt. Guidelines for the prediction of crop water requirements.
Irrigation and Drainage Paper 24, UN Food and Agriculture Organization, Rome, Italy,
1975.
[181] J. Doorenbos and W.O. Pruitt. Guidelines for the prediction of crop water requirements.
Irrigation and Drainage Paper 24, UN Food and Agriculture Organization, Rome, Italy,
1977. Second Edition.
[182] J.F. Douglas, J.M. Gasiorek, and J.A. Swaffield. Fluid Mechanics. Prentice-Hall, Upper
Saddle River, New Jersey, fourth edition, 2001.
[183] F.G. Driscoll. Ground Water and Wells. Johnson Division, St. Paul, Minnesota, second
edition, 1986.
[184] N.E. Driver. Summary of nationwide analysis of storm-runoff quality and quantity in ur-
ban watersheds. In Y. Iwasa and T. Sueishi, editors, Proceedings of the Fifth International
Conference on Urban Storm Drainage, Osaka, Japan, volume 1, pages 333–338, 1990.
[185] N.E. Driver and D.J. Lystrom. Estimation of urban storm runoff loads, urban runoff quality–
Impact and quality enhancement technology. In B. Urbonas and L.A. Roesner, editors, Pro-
ceedings of an Engineering Foundation Conference, New Hampshire, pages 222–232, Reston,
Virginia, 1986. American Society of Civil Engineers.
[186] N.E. Driver and G.D. Tasker. Techniques for estimation of storm-runoff loads, volumes, and
selected constituent concentrations in urban watersheds in the United States. Open File
Report 88-191, U.S. Geological Survey, Denver, Colorado, 1988.
[187] N.E. Driver and G.D. Tasker. Techniques for estimation of storm-runoff loads, volumes, and
selected constituent concentrations in urban watersheds in the United States. Water-Supply
Paper 2363, U.S. Geological Survey, Washington, DC, 1990.
[188] M. Duchene, E.A. McBean, and N.R. Thomson. Modeling of infiltration from trenches for
storm-water control. Journal of Water Resources Planning and Management, 120(3):276–293,
May/June 1994.
[189] J.A. Duffie and W.A. Beckman. Solar Engineering of Thermal Processes. John Wiley and
Sons, Inc., New York, 1980.
[190] T. Dunne and R.D. Black. Partial area contributions to storm runoff in a small New England
watershed. Water Resources Research, 6:1296–1311, 1970.
[191] T. Dunne and L.B. Leopold. Water in Environmental Planning. W.H. Freeman and Company,
San Francisco, California, 1978.
[192] J. Dupuit. Études Théoriques et Pratiques sur le Mouvement des Eaux dans les Canaux
DéCauverts et á Travers les Terrains Perméables. Dunod, Paris, France, second edition,
1863.

[193] H.B. Dwight. Tables of Integrals and Other Mathematical Data. Macmillan Publishing Com-
pany, New York, New York, fourth edition, 1961.
[194] B. Dziegielewski and E. Opitz. Water Demand Analysis. In L.W. Mays, editor, Urban Water
Supply Handbook, pages 5.1–5.55. McGraw-Hill Book Company, New York, New York, 2002.
[195] B. Dziegielewski, E.M. Opitz, and D. Maidment. Water Demand Analysis. In L.W. Mays,
editor, Water Resources Handbook, pages 23.1–23.62. McGraw-Hill, Inc., New York, New
York, 1996.
[196] A.A. Dzurik. Water Resources Planning. Rowman and Littlefield Publishers, Inc., Lanham,
Maryland, Third edition, 2003.
[197] P.S. Eagleson. Dynamics of flood frequency. Water Resources Research, 8:878–898, 1972.
[198] S.M. Easa. Geometric Design. In W.F. Chen, editor, The Civil Engineering Handbook, pages
2287–2319. CRC Press, Boca Raton, Florida, 1995.
[199] G. Echávez. Increase in losses coefficient with age for small diameter pipes. Journal of
Hydraulic Engineering, 123(2):157–159, February 1997.
[200] J.W. Eheart and J.R. Lund. Water-Use Management: Permit and Water-Transfer Systems.
In L.W. Mays, editor, Urban Water Supply Handbook, pages 4.1–4.41. McGraw-Hill Book
Company, New York, New York, 2002.
[201] H.A. Einstein. Der hydraulische oder profil-radius. Schweizerische Bauzeitung, 103(8):89–91,
February 1934.
[202] H.A. Einstein. The Bed Load Function for Sediment transport in Open Channel Flows.
Technical Bulletin 1026, U.S. Department of Agriculture, Washington, DC, 1950.
[203] H.A. Einstein and R.B. Banks. Fluid resistance of composite roughness. Transactions of the
American Geophysical Union, 31(4):603–610, 1951.
[204] M.Z. Ejeta and L.W. Mays. Water Pricing and Drought Management. In L.W. Mays, editor,
Urban Water Supply Handbook, pages 6.1–6.43. McGraw-Hill Book Company, New York, New
York, 2002.
[205] N. El-Jabi and S. Sarraf. Effect of maximum rainfall position on rainfall-runoff relationship.
Journal of Hydraulic Engineering, 117(5):681–685, May 1991.
[206] W.J. Elliot. Precipitation. In A.D. Ward and W.J. Elliot, editors, Environmental Hydrology,
pages 19–49. Lewis Publishers, Inc., Boca Raton, Florida, 1995.
[207] E.T. Engman. Roughness Coefficients for Routing Surface Runoff. Journal of Irrigation and
Drainage Engineering, ASCE, 112(1):39–53, 1986.
[208] Environmental and Water Resources Institute, Standardization of Reference Evapotranspi-
ration Task Committee. The ASCE Standardized Reference Evapotranspiration Equation.
Draft Report July 9, 2002, American Society of Civil Engineers, 2002.

818
[209] Environmental Protection Agency. Results of the nationwide urban runoff program, final
report. Technical Report Accession No. PB84-185552, NTIS, Washington, DC, December
1983.
[210] Environmental Protection Agency. Methodology for analysis of detention basins for control
of urban runoff quality. Technical Report EPA 440/5-87-001, U.S. Environmental Protection
Agency, Office of Water Regulations and Standards, Washington, DC, 1986.
[211] D.R. Erickson. A study of littoral groundwater seepage at Williams Lake, Minnesota using
seepage meters and wells. Master’s thesis, University of Minnesota, Minneapolis, 1981.
[212] W.H. Espey, Jr. and D.G. Altman. Nomographs for Ten-minute Unit Hydrographs for Small
Urban Watersheds. Addendum 3 of Urban Runoff Control Planning EPA-600/9-78-035, U.S.
Environmental Protection Agency, Washington, DC, 1978.
[213] W.H. Espey, Jr., D.G. Altman, and C.B. Graves. Nomographs for Ten-Minute Unit Hy-
drographs for Small Urban Watersheds. ASCE Urban Water Resources Research Program,
Technical Memorandum 32 (NTIS PB-282158), ASCE, New York, New York, 1977.
[214] C.-Y. Fan, R. Field, W.C. Pisano, J. Barsanti, J.J. Joyce, and H. Sorenson. Sewer and tank
flushing for sediment, corrosion, and pollution control. Journal of Water Resources Planning
and Management, 127(3):194–201, May/June 2001.
[215] J.A. Fay. Introduction to Fluid Mechanics. MIT Press, Cambridge, Massachusetts, 1994.
[216] Federal Emergency Management Agency. Flood insurance study guidelines and specifications
for study contractors. Report 37, FEMA, Washington, DC, 1993.
[217] Water Pollution Control Federation. Gravity Sanitary Sewer Design and Construction,
WPCF Manual of Practice No.FD-5. Water Pollution Control Federation, Washington, DC,
1982.
[218] M.C. Feller. Water balances in eucalyptus regnans, e.obliqua, and pinus radiata forests in
Victoria. Australian Forestry, 44(3):153–161, 1981.
[219] V. Ferro. Friction factor for gravel-bed channel with high boulder concentration. Journal of
Hydraulic Engineering, 125(7):771–778, July 1999.
[220] C.W. Fetter. Contaminant Hydrogeology. Prentice-Hall, Upper Saddle River, New Jersey,
second edition, 1999.
[221] C.W. Fetter. Applied Hydrogeology. Prentice-Hall, Upper Saddle River, New Jersey, fourth
edition, 2001.
[222] L. Feyen, P.J. Ribeiro Jr., F. DeSmedt, and P.J. Diggle. Stochastic delineation of capture
zones: classical versus Bayesian approach. Journal of Hydrology, 281:313–324, 2003.
[223] F.R. Fiedler. Simple, Practical Method for Determining Station Weights Using Thiessen
Polygons and Isohyetal Maps. Journal of Hydrologic Engineering, 8(4):219–221, 2003.

[224] R. Field, J.P. Heaney, and R. Pitt. Innovative Urban Wet-Weather Flow Management Sys-
tems. Technomic Publishing Company, Inc., Lancaster, Pennsylvania, 2000.
[225] E.J. Finnemore and J.B. Franzini. Fluid Mechanics with Engineering Applications. McGraw-
Hill, Inc., New York, New York, tenth edition, 2002.
[226] R.A. Fisher and L.H.C. Tippett. Limiting forms of the frequency distribution of the largest
or smallest member of a sample. Proc. Cambridge Phil. Soc., 24, part II:180–191, 1928.
[227] C.R. Fitts. Groundwater Science. Academic Press, New York, New York, 2002.
[228] Florida Geological Survey. Florida’s Ground Water Quality Monitoring Program, Hydrogeo-
logical Framework. Tallahassee, Florida, 1991. Special Publication No. 32.
[229] P. Forchheimer. Hydraulik. Teubner Verlagsgesellschaft, Stuttgart, Germany, 1930.
[230] S. Fortier and F.C. Scobey. Permissible canal velocities. Transactions of the American Society
of Civil Engineers, 89:940–984, 1926.
[231] H.A. Foster. Theoretical frequency curves and their application to engineering problems.
Transactions of the American Society of Civil Engineers, 87:142–173, 1924.
[232] R.W. Fox and A.T. McDonald. Introduction to Fluid Mechanics. John Wiley Sons, New
York, New York, fourth edition, 1992.
[233] M.A. Franklin and G.T. Losey. Magnitude and frequency of ﬂoods from urban streams in Leon
County, Florida. Water-Resources Investigations Report 84-4004, United States Geological
[234] J.B. Franzini and E.J. Finnemore. Fluid Mechanics with Engineering Applications. McGraw-
Hill, Inc., New York, New York, ninth edition, 1997.
[235] R.H. Frederick, V.A. Myers, and E.P. Auciello. Five- to 60-minute precipitation frequency
for the eastern and central United States. NOAA Technical Memorandum NWS HYDRO-35,
National Oceanic and Atmospheric Administration, National Weather Service, Silver Spring,
Maryland, June 1977.
[236] R.A. Freeze and J.A. Cherry. Groundwater. Prentice-Hall, Upper Saddle River, New Jersey,
1979.
[237] R.H. French. Open-Channel Hydraulics. McGraw-Hill, Inc., New York, New York, 1985.
[238] R.H. French. Hydraulics of Open Channel Flow. In L.W. Mays, editor, Stormwater Collection
Systems Design Handbook, pages 3.1–3.35. McGraw-Hill, Inc., New York, New York, 2001.
[239] M. Frére and G.F. Popov. Agrometeorological crop monitoring and forecasting. FAO Plant
Production and Protection Paper 17, FAO, Rome, Italy, 1979. 38-43.

820
[240] E. Ganguillet and W.R. Kutter. Versuch zur Aufstellung einer neuen allegemeinen Formel
für die gleichförmige Bewegung des Wassers in Canälen und Flüssen (An investigation to
establish a new general formula for uniform flow of water in canals and rivers). Zeitschrift des
Oesterreichischen Ingenieur- und Architekten Vereines, 21(1,2-3):6–25,46–59, 1869. (Pub-
lished as a book in Bern, Switzerland, 1877; translated into English by Rudolph Hering and
John C. Trautwine, Jr., as A general Formula for the Uniform Flow of Water in Rivers and
Other Channels John Wiley Sons, Inc., New York, 1st ed., 1888; 2d ed., 1891 and 1901).
[241] W.F. Geiger and H.R. Dorsch. Quantity-Quality Simulation (QQS): A detailed continuous
planning model for urban runoff control in Model Description, Testing and Application Vol-
ume I. Technical Report EPA-600/2-80-011, U.S. Environmental Protection Agency, Cincin-
nati, Ohio, 1980.
[242] P.M. Gerhart, R.J. Gross, and J.I. Hochstein. Fundamentals of Fluid Mechanics. Addison-
Wesley Publishing Company, Inc., Reading, Massachusetts, second edition, 1992.
[243] P.H. Gleick. An introduction to global fresh water issues. In P.H. Gleick, editor, Water in
Crisis, pages 3–12. Oxford University Press, New York, New York, 1993.
[244] GLUMB. Recommended Standards for Water Works, 1987. Great Lakes Upper Mississippi
River Board of State Public Health and Environmental Managers, Health Research, Inc.,
1987.
[245] L. Gordon. Mississippi river discharge. San Diego, California, 1992. RD Instruments.
[246] S.M. Gorelick, R.A. Freeze, D. Donohue, and J.F. Keely. Groundwater Contamination. Lewis
Publishers, Inc., Boca Raton, Florida, 1993.
[247] R.A. Granger. Fluid Mechanics. Holt, Rinehart and Winston, New York, New York, 1985.
[248] D.M. Gray, editor. Handbook on the Principles of Hydrology. National Research Council,
Port Washington, Canada, 1973. Water Information Center, Inc.
[249] Great Lakes-Upper Mississippi River Board of Sanitary Engineers. Recommended Standards
for Sewage Works. Health Education Service, Albany, New York, 1978.
[250] W.H. Green and G.A. Ampt. Studies of soil physics, Part I: The flow of air and water through
soils. J. Agric. Sci., 4(1):1–24, 1911.
[251] J.E. Gribbin. Hydraulics and Hydrology for Stormwater Management. Delmar Publishers,
Albany, New York, 1997.
[252] I.I. Gringorten. A plotting rule for extreme probability paper. Journal of Geophysical Re-
search, 68(3):813–814, 1963.
[253] T.L. Grizzard, C.W. Randall, B.L. Weand, and K.L. Ellis. Effectiveness of extended detention
ponds. In Urban Runoff Quality. American Society of Civil Engineers, 1986.
[254] E.J. Gumbel. Statistical theory of extreme values and some practical applications. Applied
Mathematics Series 33, U.S. National Bureau of Standards, Washington, DC, 1954.

[255] E.J. Gumbel. Statistics of Extremes. Columbia University Press, New York, New York, 1958.
[256] J.C.Y. Guo. Street Storm Water Conveyance Capacity. Journal of Irrigation and Drainage
Engineering, ASCE, 126(2):119–123, March/April 2000.
[257] J.C.Y. Guo. Design of Infiltration Basins for Stormwater. In L.W. Mays, editor, Stormwater
York, 2001a.
[258] R.S. Gupta. Hydrology and Hydraulic Systems. Waveland Press, Inc., Prospect Heights,
Illinois, second edition, 2001.
[259] C.T. Haan. Statistical Methods in Hydrology. The Iowa State University Press, Ames, Iowa,
1977.
[260] Haestad Methods, Inc. 1997 Practical Guide to Hydraulics and Hydrology. Haestad Press,
Waterbury, Connecticut, 1997.
[261] Haestad Methods, Inc. Computer Applications in Hydraulic Engineering. Haestad Press,
Waterbury, Connecticut, 1997.
[262] Haestad Methods, Inc. Computer Applications in Hydraulic Engineering. Haestad Press,
Waterbury, Connecticut, fifth edition, 2002.
[263] W.H. Hager. Energy Dissipators and Hydraulic Jump. Kluwer Academic Publishers, Dor-
drecht, Netherlands, 1991.
[264] W.H. Hager. Wastewater Hydraulics. Springer-Verlag, Berlin, Germany, 1999.
[265] A. Haldar and S. Mahadevan. Probability, Reliability and Statistical Methods in Engineering
Design. John Wiley Sons, New York, New York, 2000.
[266] R.L. Hall. Interception loss as a function of rainfall and forest types: stochastic modelling
for tropical canopies revisited. Journal of Hydrology, 280:1–12, 2003.
[267] E.M. Hansen. Probable maximum precipitation for design floods in the United States. Journal
of Hydrology, 96:267–278, 1987.
[268] E.M. Hansen, L.C. Schreiner, and J.F. Miller. Application of probable maximum precipitation
estimates — United States east of the 105th meridian. NOAA Hydrometeorological Report 52,
National Weather Service, Washington, DC, August 1982.
[269] M.S. Hantush. Analysis of data from pumping tests in leaky aquifers. Transactions of the
American Geophysical Union, 37(6):702–714, 1956.
[270] M.S. Hantush. Modification of the theory of leaky aquifers. Journal of Geophysical Research,
65:3713–3725, 1960.
[271] M.S. Hantush. Hydraulics of wells. In V.T. Chow, editor, Advances in Hydroscience, volume 1,
pages 281–432. Academic Press, New York, New York, 1964.

822
[272] M.S. Hantush. Growth and decay of groundwater-mounds in response to uniform percolation.
Water Resources Research, 3(1):227–234, 1967.
[273] M.S. Hantush and C.E. Jacob. Plane potential flow of ground-water with linear leakage.
Transactions of the American Geophysical Union, 35:917–936, 1954.
[274] M.S. Hantush and C.E. Jacob. Non-steady radial flow in an infinite leaky aquifer. Transactions
of the American Geophysical Union, 36(1):95–100, 1955.
[275] A.W. Harbaugh and M.G. McDonald. User’s documentation for MODFLOW-96, an update
to the U.S. Geological Survey modular finite-difference ground-water flow model. Open File
Report 96-485, United States Geological Survey, 1996.
[276] G.H. Hargreaves and Z.A. Samani. Estimating potential evapotranspiration. Journal of
Irrigation and Drainage Engineering, ASCE, 108(3):225–230, 1982.
[277] G.L. Hargreaves, G.H. Hargreaves, and J.P. Riley. Agric. benefits for Senegal River Basin.
Journal of Irrigation and Drainage Engineering, ASCE, 111(2):113–124, 1985.
[278] G.L. Hargreaves and Z.A. Samani. Reference-crop evapotranspiration from temperature.
Applied Engrg. in Agric., 1(2):96–99, 1985.
[279] D.R.F. Harleman, P.F. Melhorn, and R.R. Rumer. Dispersion-permeability correlation in
porous media. Journal of the Hydraulics Division, ASCE, 89:67–85, 1963.
[280] W.G. Harmon. Forecasting Sewage at Toledo under Dry Weather Conditions. Engineering
News Record, 80, 1918.
[281] B.W. Harrington. Design and construction of infiltration trenches. In L.A. Roesner, B. Ur-
bonas, and M.B. Sonnen, editors, Design of Urban Runoff Quality Controls, pages 291–306.
ASCE, New York, New York, 1989.
[282] L.P. Harrison. Fundamental concepts and definitions relating to humidity. In A. Wexler,
editor, Humidity and Moisture. Reinhold Publishing Company, New York, New York, 1963.
[283] J.P. Hartigan. Basis for design of wet detention basin BMP’s. In L.A. Roesner, B. Urbonas,
and M.B. Sonnen, editors, Design of Urban Runoff Quality Controls, pages 122–144. ASCE,
[284] G.A. Hathaway. Design of Drainage Facilities. Transactions of the American Society of Civil
Engineers, 110, 1945.
[285] R.H. Hawkins, A.T. Hjelmfelt, and A.W. Zevenbergen. Runoff probability, storm depth, and
curve numbers. Journal of the Irrigation and Drainage Division, ASCE, 111(4):330–340,
December 1985.
[286] A. Hazen. Discussion of “Dams on Sand Foundations, by A.C. Koenig”. Transactions of the
American Society of Civil Engineers, 73:199, 1911.

[287] J.P. Heany, W.C. Huber, and S.J. Nix. Storm water management model: Level I–Preliminary
screening procedures. Report EPA-600/2-76-275, U.S. Environmental Protection Agency,
Cincinnati, Ohio, 1976.
[288] J.P. Heany, W.C. Huber, H. Sheikh, M.A. Medina, J.R. Doyle, W.A. Peltz, and J.E. Darling.
Nationwide evaluation of combined sewer overflows and urban stormwater discharges, Volume
2, Cost assessment and impacts. Report EPA-600/2-77-064, U.S. Environmental Protection
Agency, Washington, DC, 1977.
[289] H.G. Heinemann. A New Sediment Trap Efficiency Curve for Small Reservoirs. Water
Resources Bulletin, 17:825–830, 1981.
[290] J.D. Helvey. Rainfall interception by hardwood forest litter in the Southern Appalachians.
Research Paper SE-8, U.S. Department of Agriculture, Forest Service, Southeastern Forest
Experiment Station, Asheville, NC, 1964. 9 p.
[291] J.D. Helvey. Interception by eastern white pine. Water Resources Research, 3(3):723–729,
1967.
[292] J.D. Helvey. Biological Effects in the Hydrological Cycle. In E.J. Monke, editor, Proceedings
of the Third International Seminar for Hydrology Professors, pages 103–113, West Lafayette,
IN, 1971. Purdue University.
[293] J.D. Helvey and J.J. Patric. Canopy and litter interception of rainfall by hardwoods of eastern
United States. Water Resources Research, 1:193–206, 1965.
[294] J.C. Hemain. Statistically based modelling of urban runoff quality: State of the art. In
H.C. Torno et al., editor, Urban Runoff Pollution, volume 10 of NATO ASI Ser., Ser.G,
pages 277–304. Springer-Verlag, New York, New York, 1986.
[295] H.F. Hemond and E.J. Fechner. Chemical Fate and Transport in the Environment. Academic
Press, New York, New York, 1993.
[296] F.M. Henderson. Open Channel Flow. Macmillan Publishing Co., Inc., New York, New York,
1966.
[297] H.R. Henry. Discussion of ‘Diffusion of submerged jets,’ by M.L. Albertson, Y.B. Dai, R.A.
Jensen, and H. Rouse. Transactions of the American Society of Civil Engineers, 115:687–694,
1960.
[298] J.A. Henry, K.M. Portier, and J. Coyne. The Climate and Weather of Florida. Pineapple
Press, Inc., Sarasota, Florida, 1994.
[299] J.F. Hermance. A Mathematical Primer on Groundwater Flow. Prentice-Hall, Upper Saddle
River, New Jersey, 1999.
[300] D.M. Hershfield. Rainfall Frequency Atlas of the United States for Durations from 30 Minutes
to 24 Hours and Return Periods from 1 to 100 Years. Technical Paper 40, U.S. Department
of Commerce, Weather Bureau, Washington, DC, May 1961.

824
[301] D.M. Hershfield. Method for estimating probable maximum precipitation. Journal of the
American Water Works Association, 57:965–972, 1965.
[302] A. Herzberg. Die Wasserversorgung einiger Nordseebaden (The water supply on parts of the
North Sea coast in Germany). Z. Gasbeleucht. Wasserversorg., 44:815–819, 824–844, 1901.
[303] B.L. Herzog. Slug tests for determining hydraulic conductivity of natural geologic deposits.
In D.E. Daniel and S.J. Trautwein, editors, Hydraulic Conductivity and Waste Contaminant
Transport in Soil, pages 95–110. ASTM, Philadelphia, Pennsylvania, 1994.
[304] J.D. Hewlett and A.R. Hibbert. Factors affecting the response of small watersheds to pre-
cipitation in humid areas. In W.E. Sopper and H.W. Lull, editors, Forest Hydrology, pages
275–290. Pergamon, New York, New York, 1967.
[305] W.I. Hicks. A method of computing urban runoff. Transactions of the American Society of
Civil Engineers, 109:1217, 1944.
[306] F. Hildebrand. Advanced Calculus for Applications. Prentice-Hall, Inc., Englewood Cliffs,
New Jersey, second edition, 1976.
[307] A.T. Hjelmfelt, Jr. Negative Outflows from Muskingum Flood Routing. Journal of Hydraulic
Engineering, 111(6), June 1985.
[308] A.T. Hjelmfelt, Jr. Investigation of curve number procedure. Journal of Hydraulic Engineer-
ing, 117(6):725–737, 1991.
[309] R.A. Horton. Separate roughness coefficients for channel bottom and sides. Engineering News
Record, 111(22):652–653, November 1933a.
[310] R.E. Horton. Rainfall interception. Monthly Weather Review, 47:603–623, 1919.
[311] R.E. Horton. The role of infiltration in the hydrologic cycle. Transactions of the American
Geophysical Union, 14:446–460, 1933b.
[312] R.E. Horton. Analysis of runoff-plat experiments with varying infiltration-capacity. Trans.
American Geophysical Union, 20:693–711, 1939.
[313] R.E. Horton. An approach towards physical interpretation of infiltration capacity. Soil Science
Society of America Proceedings, 5:399–417, 1940.
[314] R.E. Horton. Erosional development of streams and their drainage basins: Hydrophysical
approach to quantitative morphology. Geological Society of America Bulletin, 56:275–370,
1945.
[315] J.R.M. Hosking and J.R. Wallis. Regional Frequency Analysis. Cambridge University Press,
[316] C.H. Howe and F.P. Linaweaver. The Impact of Price on Residential Water Demand and Its
Relation to System Design and Price Structure. Water Resources Research, 13(1), February
1967.

[317] T.A. Howell, S.R. Evett, A.D. Schneider, D.A. Dusek, and K.S. Copeland. Irrigated fes-
cue grass ET compared with calculated reference grass ET. In Proceedings, Fourth National
Irrigation Symposium, pages 228–242, St. Joseph, Michigan, 2000. American Society of Agri-
cultural Engineers.
[318] W.C. Huber and R.E. Dickinson. Storm water management model, Version 4, User’s man-
ual, with addendums. Technical Report EPA-600/3-88/001a, U.S. Environmental Protection
Agency, Athens, Georgia, 1988.
[319] F.A. Huff. Characteristics and contributing causes of an abnormal frequency of flood-
producing rainstorms at Chicago. Water Resources Bulletin, 31:703–714, 1995.
[320] L. Huisman. Groundwater Recovery. Macmillan, London, 1972.
[321] B. Hunt. Dispersion model for mountain streams. Journal of Hydraulic Engineering,
125(2):99–105, February 1999.
[322] M.J. Hvorslev. Time lag and soil permeability in ground-water observation. Bulletin 36,
Waterways Experiment Station, U.S. Army Corps of Engineers, Vicksburg, Mississippi, 1951.
[323] Hydrologic Engineering Center. Probable Maximum Storm (Eastern U.S.) HMR 52, User’s
Manual. Technical report, U.S. Army Corps of Engineers, Davis, California, March 1984.
[324] Hydrologic Engineering Center. HEC-FFA Flood Frequency Analysis, Users Manual. Report
CPD-13, U.S. Army Corps of Engineers, Davis, California, 1992.
[325] Hydrologic Engineering Center. HEC-1 Flood Hydrograph Package Users Manual. Technical
report, U.S. Army Corps of Engineers, Davis, California, June 1998.
[326] Hydrologic Engineering Center. HMS Hydrologic Modeling System Technical Reference Man-
ual. Technical report, U.S. Army Corps of Engineers, Davis, California, March 2000.
[327] Hydrologic Engineering Center. HEC-HMS Hydrologic Modeling System Users Manual. Tech-
nical report, U.S. Army Corps of Engineers, Davis, California, January 2001.
[328] Insurance Services Office. Fire Suppression Rating Schedule. New York, 1980.
[329] Interagency Advisory Committee on Water Data. Guidelines for determining flood flow fre-
quency. Bulletin 17B of the Hydrology Committee, U.S. Geological Survey, Reston, Virginia,
1982.
[330] S. Irmak, R.G. Allen, and E.B. Whitty. Daily grass and alfalfa-reference evapotranspiration
estimates and alfalfa-to-grass evapotranspiration ratios in Florida. Journal of Irrigation and
Drainage Engineering, ASCE, 129(5):360–370, 2003c.
[331] S. Irmak, A. Irmak, R.G. Allen, and J.W. Jones. Solar and Net Radiation-Based Equations
to Estimate Reference Evapotranspiration in Humid Climates. Journal of Irrigation and
Drainage Engineering, ASCE, 129(5):336–347, September/October 2003b.

826
[332] S. Irmak, A. Irmak, J.W. Jones, T.A. Howell, J.M. Jacobs, R.G. Allen, and G. Hoogenboom.
Predicting Daily Net Radiation Using Minimum Climatological Data. Journal of Irrigation
and Drainage Engineering, ASCE, 129(4):256–269, July/August 2003a.
[333] S.A. Isiorho and J.H. Meyer. The effects of bag type and meter size on seepage meter
measurements. Ground Water, 37:411–413, 1999.
[334] O.W. Israelsen and R.C. Reeve. Canal lining experiments in the Delta Area. Utah Technical
Bulletin 313, Utah Agricultural Experiment Station, Logan, Utah, 1944.
[335] D. Itenfisu, R.L. Elliott, R.G. Allen, and I.A. Walter. Comparison of Reference Evapotran-
spiration Calculations as Part of the ASCE Standardization Effort. Journal of Irrigation and
Drainage Engineering, ASCE, 129(6):440–448, November/December 2003.
[336] C.F. Izzard. The surface-profile of overland flow. Transactions of the American Geophysical
Union, 25:959–969, 1944.
[337] C.F. Izzard. Hydraulics of Runoff from Developed Surfaces. Proceedings of the Highway
Research Board, 26:129–146, 1946.
[338] C.R. Jackson, S.J. Burges, X. Liang, K.M. Leytham, K.R. Whiting, D.M. Hartley, C.W.
Crawford, B.N. Johnson, and R.R. Horner. Development and Application of Simplified Con-
tinuous Hydrologic Modeling for Drainage Design and Analysis. In M.S. Wigmosta and
S.J. Burges, editors, Land Use and Watersheds, pages 39–58. American Geophysical Union,
Washington, DC, 2001.
[339] I.J. Jackson. Problems of throughfall and interception assessment under tropical forest. Jour-
nal of Hydrology, 12:234–254, 1971.
[340] Jackson and others. Contaminant hydrogeology of toxic organic chemicals at a disposal site,
Gloucester, Ontario. 1. Chemical concepts and site assessment. Iwd scientific series 141,
Environment Canada, 1985. 114 p.
[341] C.E. Jacob. Drawdown test to determine effective radius of artesian well. Transactions of
the American Society of Civil Engineers, 112:1047–1064, 1947. Paper 2321.
[342] A.K. Jain. Accurate explicit equation for friction factor. ASCE, Journal of the Hydraulics
Division, 102(HY5):674–677, May 1976.
[343] A.K. Jain, D.M. Mohan, and P. Khanna. Modified Hazen-Williams formula. Journal of the
Environmental Engineering Division, ASCE, 104(EE1):137–146, February 1978.
[344] S.C. Jain. Open-Channel Flow. John Wiley Sons, New York, New York, 2001.
[345] S.V. Jakovlev, J.A.A. Karelm, A.I. Zukov, and S. Kolobanov. Kanalizacja. Stroizdat, Moscow,
1975.
[346] L.D. James and R.R. Lee. Economics of Water Resources Planning. McGraw-Hill, Inc., New

[347] W.S. Janna. Introduction to Fluid Mechanics. PWS-KENT Publishing Company, Boston,
Massachusetts, third edition, 1993.
[348] A.F. Jenkinson. The frequency distribution of the annual maximum (or minimum) value
of meteorological elements. Quarterly Journal of Royal Meteorological Society, 81:158–171,
1955.
[349] M.E. Jennings, W.O. Thomas, and H.C. Riggs. Nationwide Summary of U.S. Geological
Survey Regional Regresson Equations for Estimating Magnitude and Frequency of Floods
for Ungaged Sites. Water-Resources Investigations Report 94-4002, United States Geological
[350] S.W. Jens. Design of urban highway drainage- The state of the art. Report FHWA-TS-79-
225, U.S. Department of Transportation, Federal Highway Administration, Washington, DC,
1979.
[351] M.E. Jensen. Empirical methods of estimating or predicting evapotranspiration using radia-
tion. In Proceedings of Conference on Evapotranspiration, pages 57–61, 64, Chicago, Illinois,
December 1966. American Society of Agricultural Engineers.
[352] M.E. Jensen and H.R. Haise. Estimating evapotranspiration from solar radiation. Journal of
Irrigation and Drainage Engineering, ASCE, 89:15–41, 1963.
[353] M.E. Jensen, R.D.Burman, and R.G. Allen, editors. Evapotranspiration and Irrigation Water
Requirements. American Society of Civil Engineers, New York, New York, 1990. Manual of
Practice No.70.
[354] M.E. Jensen, J.L. Wright, and B.J. Pratt. Estimating soil moisture depletion from climate,
crop, and soil data. Transactions of the American Society of Agricultural Engineers, 14:954–
959, 1971.
[355] T.K. Jewell and D.D. Adrian. Development of improved stormwater quality models. Journal
of the Environmental Engineering Division, ASCE, 107:957–974, 1981.
[356] T.K. Jewell and D.D. Adrian. Statistical analysis to derive improved stormwater quality
models. Journal of the Water Pollution Control Federation, 54:489–499, 1982.
[357] R.C. Johanson, J.C. Imhoﬀ, J.L. Kittle, and S. Donigan. Hydrologicaal Simulation Program-
Fortran (HSPF): User manual for release 8.0. Technical Report EPA/600/3-84/066, U.S.
Environmental Protection Agency, Athens, Georgia, 1984.
[358] D. Johnson. Down the Drain. Los Angeles Times, V1, February 2, 1988.
[359] D. Johnson, M. Smith, V. Koren, and B. Finnerty. Comparing mean areal precipitation esti-
mates from NEXRAD and rain gage networks. Journal of Hydrologic Engineering, 4(2):117–
124, April 1999.
[360] F.L. Johnson and F.M. Chang. Drainage of highway pavements. Hydraulic Engineering
Circular 12, Federal Highway Administration, McLean, VA, 1984.

828
[361] J.L. Johnson. Local wellhead protection in Florida. Technical report, City of Tallahassee,
Water Quality Division, Aquifer Protection Section, Tallahassee, Florida, 1997.
[362] P.A. Johnson. Uncertainty in hydraulic parameters. Journal of Hydraulic Engineering,
22(2):112–114, February 1996.
[363] C. Jothityangkoon and M. Sivapalan. Towards estimation of extreme floods: examination of
the roles of runoff process changes and floodplain flows. Journal of Hydrology, 281:206–229,
2003.
[364] A.G. Journel. Fundamentals of Geostatistics in Five Lessons, volume 8 of Short Course in
Geology. American Geophysical Union, Washington, DC, 1989.
[365] Z.J. Kabala. Well response in a leaky aquifer and computational interpretation of pumping
tests. In W.S. Hsieh, S.T. Su, and F. Wen, editors, Hydraulic Engineering, Proceedings
of ASCE National Conference on Hydraulic Engineering and International Symposium on
Engineering Hydrology, page 21, New York, New York, 1993. ASCE.
[366] A.I. Kashef. Groundwater Engineering. McGraw-Hill Book Company, Inc., New York, New
York, 1986.
[367] M. Kay. Practical Hydraulics. E FN Spon, London, England, 1998.
[368] M.W. Kemblowki and G.E. Urroz. Subsurface flow and transport. In L.W. Mays, editor,
Hydraulic Design Handbook, pages 4.1–4.26. McGraw-Hill Book Company, New York, New
York, 1999.
[369] W.S. Kerby. Time of Concentration for Overland Flow. Civil Engineering, 29(3):174, March
1959.
[370] G.H. Keulegan. Laws of turbulent flow in open channels. Journal of Research of N.B.S.,
21:707–741, 1938.
[371] D.F. Kibler. Desk-top runoff methods. In D.F. Kibler, editor, Urban Stormwater Hydrology,
pages 87–135. American Geophysical Union, Water Resources Monograph Series, Washington,
DC, 1982.
[372] G.J. Kirmeyer, L. Kirby, B.M. Murphy, P.F. Noran, K. Martel, T.W. Lund, J.L. Anderson,
and R. Medhurst. Maintaining Water Quality in Finished Water Storage Facilities. AWWA
Research Foundation and American Water Works Association, Denver, CO, 1999.
[373] P.Z. Kirpich. Time of Concentration of Small Agricultural Watersheds. Civil Engineering,
10(6):362, June 1940.
[374] G.W. Kite. Frequency and Risk Analysis in Hydrology. Water Resources Publications, Fort
Collins, Colorado, 1977.
[375] R.T. Knapp, J.W. Daily, and F.G. Hammitt. Cavitation. McGraw-Hill, Inc., New York, New
York, 1970.

[376] S.F. Korom, K.F. Bekker, and O.J. Helweg. Influence of Pump Intake Location on Well
Efficiency. Journal of Hydrologic Engineering, 8(4):197–203, July/August 2003.
[377] N.T. Kottegoda and R. Rosso. Statistics, Probability, and Reliability for Civil and Environ-
mental Engineers. McGraw-Hill, Inc., New York, New York, 1997.
[378] D. Koutsoyiannis. A probabilistic view of Hershfield’s method for estimating probable maxi-
mum precipitation. Water Resources Research, 35(4):1313–1322, April 1999.
[379] N. Kouwen, R.M. Li, and D.B. Simons. Velocity measurements in a channel lined with flexible
plastic roughness elements. Technical report, Department of Civil Engineering, Colorado
State University, Fort Collins, Colorado, 1980. Technical Report No. CER79-80-RML-DBS-
11.
[380] J. Kozeny. Über Kapillare Leitung des Wassers im Boden. Sitzungsber. Akad. Wiss., 36:271–
306, 1927. (in German).
[381] J. Kozeny. Theorie und Berechnung der Brunnen. Wasserkraft und Wassenwirtschaft, 28:88–
92, 101–105, 113–116, 1933. (in German).
[382] M. Krishnamurthy and B.A. Christensen. Equavalent roughness for shallow channels. Journal
of the Hydraulics Division, ASCE, 98(12):2257–2263, 1972.
[383] W.C. Krumbein and G.D. Monk. Permeability as a function of the size parameters of uncon-
solidated sand. Am. Inst. Min. Met. Eng. Tech. Pub., 150(11):1492, 1942.
[384] W.C. Krumbein and G.D. Monk. Permeability as a function of the size parameters of uncon-
solidated sand. Am. Inst. Min. Met. Eng. Tech. Pub., 151:153–163, 1943.
[385] E. Kuichling. The Relation Between the Rainfall and the Discharge of Sewers in Populous
Districts. Transactions of the American Society of Civil Engineers, 20:1–56, 1889.
[386] A.L. Lagvankar and J.P. Velon. Wastewater and stormwater piping systems. In M.L. Nayyar,
editor, Piping Handbook, pages C.619–C.665. McGraw-Hill Book Company, New York, New
York, seventh edition, 2000.
[387] E.W. Lane. Design of stable channels. Transactions of the American Society of Civil Engi-
neers, 120:1234–1279, 1955.
[388] K. Lansey and W. El-Shorbagy. Design of Pumps and Pump Facilities. In L.W. Mays, editor,
Stormwater Collection Systems Design Handbook, pages 12.1–12.41. McGraw-Hill, Inc., New
[389] K. Lansey and L.M. Mays. Hydraulics of Water Distribution Systems. In L.W. Mays, editor,
Hydraulic Design Handbook, pages 9.1–9.38. McGraw-Hill Book Company, New York, New
York, 1999.
[390] B.E. Larock, R.W. Jeppson, and G.Z. Watters. Hydraulics of Pipeline Systems. CRC Press,
Inc., Boca Raton, Florida, 2000.

830
[391] G. Leclerc and J.C. Schaake. Derivation of hydrologic frequency curves. Report 142, R.M.
Parsons Laboratory of Hydrodynamics and Water Resources, Massachusetts Institute of Tech-
nology, Cambridge, Massachusetts, 1972.
[392] D.R. Lee. A device for measuring seepage flux in lakes and estuaries. Limnol. Oceanogr.,
22:140–147, 1977.
[393] J.G. Lee and J.P. Heany. Estimation of Urban Imperviousness and its Impacts on Storm
Water Systems. Journal of Water Resources Planning and Management, 129(5):419–426,
September/October 2003.
[394] T.-C. Lee. Applied Mathematics in Hydrogeology. Lewis Publishers, Inc., Boca Raton, Florida,
1999.
[395] J. Lehr, S. Hurlburt, B. Gallagher, and J. Voytek. Design and Construction of Water Wells,
A Guide for Engineers. Van Nostrand Reinhold, New York, New York, 1988.
[396] D.H. Lennox. Analysis of step-drawdown test. Journal of the Hydraulics Division, ASCE,
92(HY6):25–48, 1966.
[397] B. Levy and R. McCuen. Assessment of storm duration for hydrologic design. Journal of
Hydrologic Engineering, 4(3):209–213, July 1999.
[398] L. Leyton, E.R.C. Reynolds, and F.B. Thompson. Rainfall interception in forest and moor-
land. In W.E. Sopper and H.W. Lull, editors, International symposium on forest hydrology;
1965 August 29 - September 10; Pennsylvania State University, University Park, PA, pages
163–178. Oxford: Pergamon Press, 1967.
[399] J.A. Liggett. Fluid Mechanics. McGraw-Hill, Inc., New York, New York, 1994.
[400] J.T. Limerinos. Determination of the Manning Coefficient from Measured Bed Roughness in
Natural Channels. Water-Supply Paper 1898-B, U.S. Geological Survey, Washington, DC,
1970.
[401] C.H. Lin, J.F. Yean, and C.T. Tsai. Influence of Sluice Gate Contraction Coefficient on Distin-
guishing Condition. Journal of Irrigation and Drainage Engineering, ASCE, 128(4):249–252,
July/August 2002.
[402] S.S.T. Lin and W.A. Perkins. Review of pre-development runoff analysis methods, Volume
I. Report DRE 270, South Florida Water Management District, West Palm Beach, Florida,
1989.
[403] R.K. Linsley, J.B. Franzini, D.L. Freyberg, and G. Tchobanoglous. Water-Resources Engi-
neering. McGraw-Hill, Inc., New York, New York, fourth edition, 1992.
[404] R.K. Linsley, M.A. Kohler, and J.L.H. Paulhus. Hydrology for Engineers. McGraw-Hill, Inc.,
New York, New York, third edition, 1982.
[405] C.P. Liou. Limitations and proper use of the Hazen-Williams equation. Journal of Hydraulic
Engineering, 124(9):951–954, September 1998.

[406] D.E. Lloyd-Davies. The elimination of storm water from sewerage systems. Proc. Inst. Civ.
Eng., 164:41–67, 1906.
[407] G.V. Loganathan, D.F. Kibler, and T.J. Grizzard. Urban Stormwater Management. In L.W.
Mays, editor, Water Resources Handbook, pages 26.1–26.35. McGraw-Hill, Inc., New York,
New York, 1996.
[408] S.W. Lohman. Ground-water hydraulics. Professional Paper 708, U.S. Geological Survey,
1972.
[409] M.A. Lopez and W.M. Woodham. Magnitude and frequency of flooding on small urban
watersheds in the Tampa Bay area, west-central Florida. Water-Resources Investigations
Report 82-42, United States Geological Survey, Reston, Virginia, 1982.
[410] G.K. Lotter. Considerations of hydraulic design of channels with different roughness of walls.
Trans. All Union Scientific Research, Institute of Hydraulic Engineering, 9:238–241, 1933.
[411] D.P. Loucks. Surface-Water Quality Management Models. In A.K. Biswas, editor, Systems
Approach to Water Management. McGraw-Hill Book Company, New York, New York, 1976.
[412] W. Maddaus, G. Gleason, and J. Darmody. Integrating Conservation into Water Supply Plan-
ning: How can water suppliers achieve an appropriate balance between capacity expansion
and conservation? Journal of the American Water Works Association, November 1996.
[413] R. Manning. Flow of water in open channels and pipes. Trans. Inst. Civil Engrs. (Ireland),
20, 1890.
[414] A. Mantoglou. Pumping management of coastal aquifers using analytic models of saltwater
intrusion. Water Resources Research, 39(12), 1335, doi:10.1029/2002WR001891, 2003.
[415] J. Marsalek. Calibration of the tipping bucket raingage. Journal of Hydrology, 53:343–354,
1981.
[416] D.L. Martin and J. Gilley. Irrigation Water Requirements. In National Engineering Handbook,
chapter 2, part 623. U.S. Department of Agriculture, Natural Resources Conservation Service,
1993.
[417] E.S. Martins and J.R. Stedinger. Generalized maximum-liklihood generalized extreme-value
quantile estimators for hydrologic data. Water Resources Research, 36(3):737–744, March
2000.
[418] L.W. Mays. Water Resources: An Introduction. In L.W. Mays, editor, Water Resources
Handbook, pages 1.3–1.35. McGraw-Hill, Inc., New York, New York, 1996.
[419] L.W. Mays. Introduction. In L.W. Mays, editor, Water Distribution Systems Handbook,
pages 1.1–1.30. McGraw-Hill Book Company, New York, New York, 2000.
[420] L.W. Mays. Water Resources Engineering. John Wiley Sons, New York, New York, 2001.
[421] G.T. McCarthy. The unit-hydrograph and flood routing. Unpublished article at U.S. Army
Corps of Engineers North Atlantic Division Conference, 1938.

832
[422] R.H. McCuen. Hydrologic Analysis and Design. Prentice-Hall, Upper Saddle River, New
Jersey, 1989.
Jersey, second edition, 1998.
[424] R.H. McCuen. Do water resources engineers need factors of safety for design? Journal of
Water Resources Planning and Management, 127(1):4–5, 2001.
[425] R.H. McCuen. Modeling Hydrologic Change: Statistical Methods. Lewis Publishers, Inc.,
Boca Raton, Florida, 2002a.
Jersey, third edition, 2005.
[427] R.H. McCuen and R.E. Beighley. Seasonal flow frequency analysis. Journal of Hydrology,
279:43–56, 2003.
[428] R.H. McCuen, P.A. Johnson, and R.M. Ragan. Hydrology. Technical Report HDS-2, U.S.
Federal Highway Administration, Washington, DC, September 1996.
[429] R.H. McCuen and O. Okunola. Extension of TR-55 for Microwatersheds. Journal of Hydro-
logic Engineering, 7(4):319–325, July/August 2002.
[430] R.H. McCuen, S.L. Wong, and W.J. Rawls. Estimating urban time of concentration. Journal
of Hydraulic Engineering, 110(7):887–904, 1984.
[431] M.G. McDonald and A.W. Harbaugh. A modular three-dimensional finite-difference ground-
water flow model. Techniques of Water Resources Investigations of the United States Geo-
logical Survey, Book 6, Chapter A1, U.S. Geological Survey, Reston, Virginia, 1988.
[432] B.M. McEnroe. Characteristics of intense storms in Kansas. In World Water Issues in
Evolution, pages 933–940. ASCE, New York, New York, 1986.
[433] T.J. McGhee. Water Supply and Sewerage. McGraw-Hill, Inc., New York, New York, sixth
edition, 1991.
[434] R.G. Mein and C.L. Larson. Modeling infiltration during a steady rain. Water Resources
Research, 9(2):384–394, 1973.
[435] R.A. Meriam. A note on the interception loss equation. Journal of Geophysical Research,
65:3850–3851, 1960.
[436] Metcalf Eddy, Inc. Wastewater Engineering: Collection and Pumping of Wastewater.
McGraw-Hill, Inc., New York, New York, 1981.
[437] P.E. Meyer-Peter and R. Muller. Formulas for Bed Load Transport. In Proceedings of the
Third International Association for Hydraulic Research, Stockholm, Sweden, pages 39–64,
1948.

[438] Miami-Dade Public Works Department. Public Works Manual, Part 2: Design and Con-
struction, 2001.
[439] D.W. Miller, J.J. Geraghty, and R.S. Collins. Water Atlas of the United States. Water
Information Center, Inc., Port Washington, New York, 1962.
[440] J.F. Miller. Probable maximum precipitation and rainfall frequency data for Alaska. Technical
report, U.S. Department of Commerce, Weather Bureau, Washington, DC, 1963.
[441] J.F. Miller, R.H. Frederick, and R.J. Tracey. Precipitation frequency atlas of the western
United States. NOAA Atlas 2, U.S. National Weather Service, Silver Springs, MD, 1973. 11
Volumes.
[442] N. Miller and R. Cronshey. Runoff curve numbers – the next step. In B.C. Yen, editor, Channel
Flow and Catchment Runoff, pages 910–916. Department of Civil Engineering, University of
Virginia, Charlottseville, Virginia, 1989.
[443] S.K. Mishra, J.V. Tyagi, and V.P. Singh. Comparison of infiltration models. Hydrological
Processes, 17:2629–2652, August 2003.
[444] J.L. Monteith. Evaporation and the environment. Symp. Soc. Expl. Biol., 19:205–234, 1965.
[445] J.L. Monteith. Principles of Environmental Physics. Edward Arnold, London, 1973.
[446] J.L. Monteith. Evaporation and surface temperature. Quarterly Journal of Royal Meteoro-
logical Society, 107:1–27, 1981.
[447] S. Montes. Hydraulics of Open Channel Flow. ASCE Press, Reston, Virginia, 1998.
[448] J.H. Montgomery. Groundwater Chemicals Desk Reference. Lewis Publishers, Inc., Boca
Raton, Florida, 3 edition, 2000.
[449] L.F. Moody. Friction Factors for Pipe Flow. Trans. ASME, 66(8), 1944.
[450] L.F. Moody. Some Pipe Characteristics of Engineering Interest. Houille Blanche, May-June
1950.
[451] L.F. Moody and T. Zowski. Hydraulic Machinery. In C.V. Davis and K.E. Sorensen, editors,
Handbook of Applied Hydraulics. McGraw-Hill, Inc., New York, New York, third edition, 1989.
[452] H.J. Morel-Seytoux and J.P. Verdin. Extension of Soil Conservation Service rainfall runoff
methodology for ungaged watersheds. Report FHWA/RD-81/060, Federal Highway Admin-
istration, Washington, DC, 1981.
[453] R. Morgan and D.W. Hulinghorst. Unit Hydrographs for Gauged and Ungauged Watersheds.
Technical report, U.S. Engineers Office, Binghampton, New York, July 1939.
[454] D.A. Morris and A.I. Johnson. Summary of hydrologic and physical properties of rock and soil
materials, as analysed by the Hydrologic Laboratory of the U.S. Geologic Survey, 1948-1960.
Water-Supply Paper 1839-D, U.S. Geological Survey, 1967.

834
[455] A.K. Motayed and M. Krishnamurthy. Composite roughness of natural channels. Journal of
the Hydraulics Division, ASCE, 106(6):1111–1116, 1980.
[456] R.L. Mott. Applied Fluid Mechanics. Merrill, New York, New York, 1994.
[457] L. Muhlhofer. Rauhigkeitsuntersuchungen in einem stollen mit betonierter sohle und un-
verkleideten wanden. Wasserkraft und Wasserwirtschaft, 28(8):85–88, 1933.
[458] T.J. Mulvaney. On the use of self-registering rain and flood gauges in making observations
on the relations of rainfall and flood discharges in a given catchment. Trans. Inst. Civ. Eng.
Ireland, 4(2):18–31, 1850.
[459] B.R. Munson, D.F. Young, and T.H. Okiishi. Fundamentals of Fluid Mechanics. John Wiley
Sons, New York, New York, second edition, 1994.
[460] L.C. Murdoch and S.E. Kelly. Factors affecting the performance of conventional seepage
meters. Water Resources Research, 39(6), 1163, doi:10.1029/2002WR001347, 2003.
[461] T.E. Murphy. Spillway Crest Design. Misc. Paper H-73-5, Waterways Experiment Station,
U.S. Army Corps of Engineers, Vicksburg, MS, 1973.
[462] M. Muskat. Potential distribution in large cylindrical discs (homogeneous sands) with par-
tially penetrating electrodes (partially penetrating wells). Physics, 2(5):329–384, 1932.
[463] M. Muskat. The Flow of Homogeneous Fluids through Porous Media. McGraw-Hill, Inc., New
[464] W.R.C. Myers. Influence of geometry on discharge capacity of open channels. Journal of
Hydraulic Engineering, 117(5):676–680, May 1991.
[465] S. Naoum and I.K. Tsanis. Temporal and spatial variation of annual rainfall on the island of
Crete, Greece. Hydrological Processes, 17:1899–1922, 2003.
[466] National Research Council. Safety of dams, flood and earthquake criteria. National Academy
Press, Washington, DC, 1985.
[467] National Research Council. Opportunities in the Hydrologic Sciences. National Academy
Press, Washington, DC, 1991.
[468] National Weather Service (NWS). NWSRFS User’s
Manual Documentation, Release Number 64, June 2002.
http://www.nws.noaa.gov/oh/hrl/nwsrfs/users manual/htm/xrfsdochtm.htm.
[469] L.C. Neale and R.E. Price. Flow characteristics of PVC sewer pipe. Journal of the Sanitary
Engineering Division, ACSE, 90(SA3):109, 1964.
[470] S.P. Neuman. Theory of flow in unconfined aquifers considering delayed response of the water
table. Water Resources Research, 8(4):1031–1045, August 1972.
[471] S.P. Neuman. Supplementary comments on ‘Theory of flow in unconfined aquifers considering
delayed response of the water table’. Water Resources Research, 9:1102–1103, 1973.

[472] S.P. Neuman. Analysis of pumping test data from anisotropic unconfined aquifers considering
delayed gravity response. Water Resources Research, 11:329–342, 1975.
[473] S.P. Neuman and P.A. Witherspoon. Theory of flow in aquicludes adjacent to slightly leaky
aquifers. Water Resources Research, 4(1):103–112, 1968.
[474] S.P. Neuman and P.A. Witherspoon. Theory of flow in a confined two aquifers system. Water
Resources Research, 5(2):803–816, 1969a.
[475] S.P. Neuman and P.A. Witherspoon. Applicability of current theories of flow in leaky aquifers.
Water Resources Research, 5(4):817–829, 1969b.
[476] S.P. Neuman and P.A. Witherspoon. Field determination of the hydraulic properties of leaky
multiple aquifer systems. Water Resources Research, 8(5):1284–1298, 1972.
[477] B.D. Newport. Salt water intrusion in the United States. Technical Report 600/8-77-011,
U.S. Environmental Protection Agency, Washington, DC, 1977.
[478] V. Nguyen and G.F. Pinder. Direct calculation of aquifer parameters in slug test analy-
sis. In J. Rosenshein and G.D. Bennett, editors, Groundwater Hydraulics, Water Resources
Monograph 9, pages 222–239. American Geophysical Union, 1984.
[479] J.W. Nicklow. Design of Stormwater Inlets. In L.W. Mays, editor, Stormwater Collection
Systems Design Handbook, pages 5.1–5.42. McGraw-Hill, Inc., New York, New York, 2001.
[480] J. Niemczynowicz. The dynamic calibration of tipping-bucket raingauges. Nord. Hydrol.,
17:203–214, 1986.
[481] J. Nikuradse. Gesetzmässigkeiten der turbulenten strömung in glatten röhren. VDI-
Forschungsh, 356, 1932.
[482] J. Nikuradse. Strömungsgesetze in rauhen Röhren. VDI-Forschungsh, 362, 1933.
[483] N.S. Norman, E.J. Nelson, and A.K. Zundel. Improved Process for Foodplain Delineation from
Digital Terrain Models. Journal of Water Resources Planning and Management, 129(5):427–
436, September/October 2003.
[484] M.A. Nouh and R.D. Townsend. Shear stress distribution in stable channel bends. Journal
of the Hydraulics Division, ASCE, 105(HY10):1233–1245, October 1979.
[485] P. Novak. Improvement of water quality in rivers by aeration at hydraulic structures. In
M. Hino, editor, Water Quality and its Control, pages 147–168. A.A. Balkema Publishers,
Brookfield, Vermont, 1994.
[486] V. Novotny, K.R. Imhoff, M. Olthof, and P.A. Krenkel. Karl Imhoff’s Handbook of Urban
Drainage and Wastewater Disposal. John Wiley Sons, New York, New York, 1989.
[487] E. Nyer, G. Boettcher, and B. Morello. Using the properties of organic compounds to help
design a treatment system. Ground Water Monitoring Review, 11(4):115–120, 1991.

836
[488] J.E. O’Connor and J.E. Costa. Spatial distribution of the largest rainfall-runoff floods from
basins between 2.6 and 26,000 km2 in the United States and Puerto Rico. Water Resources
Research, 40, W01107, doi:10.1029/2003WR002247, 2004.
[489] American Society of Civil Engineers. Quality of Ground Water, Guidelines for Selection and
Application of Frequently Used Models. American Society of Civil Engineers, New York, New
York, 1996. Manual of Practice No.85.
[490] National Academy of Sciences. Safety of Existing Dams: Evaluation and Improvement. Na-
tional Academy Press, Washington, DC, 1983.
[491] I.C. Olmsted. Stomatal resistance and water stress in melaleuca. Final Report, Contract
with USDA, Forest Service, August 1978.
[492] R.M. Olson and S.J. Wright. Essentials of Engineering Fluid Mechanics. Harper Row,
Publishers, Inc., New York, New York, fifth edition, 1990.
[493] P.S. Osbourne. Suggested operating procedures for aquifer pumping tests. EPA Ground
Water Issue EPA/540/S-93/503, U.S. Environmental Protection Agency, February 1993.
[494] D.E. Overton and M.E. Meadows. Storm Water Modeling. Academic Press, New York, New
York, 1976.
[495] J.N. Paine and A.O. Akan. Design of Detention Systems. In L.W. Mays, editor, Stormwater
York, 2001.
[496] W.C. Palmer. Meteorological Drought. Technical Report Research Paper No. 45, U.S. De-
partment of Commerce, Weather Bureau, 1965.
[497] J.F. Pankow and J.A. Cherry. Dense Chlorinated Solvents and other DNAPLs in Grounwater.
Waterloo Press, Portland Oregon, 1996.
[498] I.S. Papadopulos and H.H. Cooper, Jr. Drawdown in a well of large diameter. Water Resources
Research, 3(1):241–244, 1967.
[499] N.N. Pavlovskii. K Voporosu o Raschetnoi dlia Ravnomernogo Dvizheniia v Vodotokahk s
Neodnorodnymi Stenkami (On a design formula for uniform flow in channels with nonho-
mogeneous walls). Izvestiia Vsesoiuznogo Nauchno-Issledovatel’skogo Instituta Gidrotekhniki
(Trans. All-Union Sci. Res. Inst. Hydraulic Eng.), 3:157–164, 1931.
[500] K. Pearson. Tables for Statisticians and Biometricians. Columbia University Press, New
York, New York, third edition, 1930.
[501] R. Pecher. The runoff coefficient and its dependence on rain duration. Berichte aus dem
Institut fur Wasserwirtschaft und Gesundheitsingenieurwesen, No.2, 1969. TU Munich.
[502] H. Penman. Natural evaporation from open water, bare soil, and grass. Proc. R. Soc. A.,
A193:120–146, 1948.

[503] H.L. Penman. Evaporation: An introductory survey. Netherlands Journal of Agricultural
Sciences, Series A, 4:9–29, 1956.
[504] H.L. Penman. Vegetation and hydrology. Technical Communication 53, Commonwealth
Bureau of Soils, Harpenden, England, 1963. 125pp.
[505] L.S. Pereira, A. Perrier, R.G. Allen, and I. Alves. Evapotranspiration: Concepts and future
trends. Journal of Irrigation and Drainage Engineering, ASCE, 125(2):45–51, 1999.
[506] J.R. Philip. An infiltration equation with physical significance. Soil Science, 77:153–157,
1954.
[507] J.R. Philip. Variable-head ponded infiltration under constant or variable rainfall. Water
Resources Research, 29(7):2155–2165, July 1993.
[508] N.N. Pillai. Effect of shape on uniform flow through smooth rectangular open channels.
Journal of Hydraulic Engineering, 123(7):656–658, July 1997.
[509] R.D. Pomeroy and J.D. Parkhurst. The forecasting of sulfide buildup rates in sewers. Progress
in Water Technology, 9, 1977.
[510] V.M. Ponce. Engineering Hydrology, Principles and Practices. Prentice-Hall, Upper Saddle
River, New Jersey, 1989.
[511] V.M. Ponce, A.K. Lohani, and P.T. Huston. Surface albedo and water resources: Hydro-
climatological impact of human activities. Journal of Hydrologic Engineering, 2(4):197–203,
October 1997.
[512] V.M. Ponce, R.P. Pandey, and Sezar Ercan. Characterization of drought across climatic
spectrum. Journal of Hydrologic Engineering, 5(2):222–224, April 2000.
[513] M.C. Potter and D.C. Wiggert. Mechanics of Fluids. Prentice-Hall, Upper Saddle River,
New Jersey, 1991.
[514] M.C. Potter and D.C. Wiggert. Mechanics of Fluids. Brooks/Cole, Pacific Grove, California,
third edition, 2001.
[515] A. Prakash. Water Resources Engineering. ASCE Press, New York, New York, 2004.
[516] C.H.B. Priestly and R.J. Taylor. On the assessment of surface heat flux and evaporation
using large-scale parameters. Mon. Weath. Rev., 100:81–92, 1972.
[517] L.G. Puls. Construction of flood flow routing curves, 1928. US 70th Congress, First Session,
House Document 185, pp.46-52, and US 71st Congress, Second Session, House Document 328,
pp.190-191.
[518] V.L. Quisenberry and R.E. Phillips. Percolation of surface-applied water in the field. Soil
Sci. Soc. Am. J., 40:484–489, 1976.

838
[519] M. Radojkovic and C. Maksimovic. On standardization of computational models for overland
flow. In B.C. Yen, editor, Proceedings of the Fourth International Conference on Urban
Storm Drainage, pages 100–105, Lausanne, Switzerland, 1987. International Association for
Hydraulic Research.
[520] C.D. Rail. Groundwater Contamination. Technomic Publishing Company, Inc., Lancaster,
Pennsylvania, 1989.
[521] N. Rajaratnam and K. Subramanya. Flow equation for the sluice gate. Journal of Irrigation
and Drainage Engineering, ASCE, 93(3):167–186, 1967.
[522] C.E. Ramser. Runoff from Small Agricultural Areas. Journal of Agricultural Research, 34(9),
1927.
[523] R.E. Rathbun. Transport, behavior, and fate of volatile organic compounds in streams.
Professional Paper 1589, U.S. Geological Survey, Washington, DC, 1998.
[524] A.J. Raudkivi and R.A. Callander. Analysis of Groundwater Flow. John Wiley Sons, Inc.,
[525] W. Rawls, P. Yates, and L. Asmussen. Calibration of selected infiltration equations for
the Georgia Coastal Plain. Technical Report ARS-S-113, U.S. Department of Agriculture,
Agricultural Research Service, Washington, DC, 1976.
[526] W.J. Rawls and D.L. Brakensiek. Estimating soil water retention from soil properties. Journal
of Irrigation and Drainage Engineering, ASCE, 108(2):166–171, 1982.
[527] W.J. Rawls, D.L. Brakensiek, and N. Miller. Green-Ampt infiltration parameters from soils
data. Journal of Hydraulic Engineering, 109(1):1316–1320, 1983.
[528] W.J. Rawls, D.L. Brakensiek, and K.E. Saxton. Estimation of Soil Water Properties. Trans-
actions of the American Society of Agricultural Engineers, 25(5):1316–1320, 1328, 1982.
[529] A.J. Reese and S.T. Maynord. Design of Spillway Crest. Journal of Hydraulic Engineering,
113(4):476–490, 1987.
[530] O. Reynolds. An experimental investigation of the circumstances which determine whether
the motion of water shall be direct or sinuous and of the law of resistance in parallel channel.
Philosophical Transactions, Royal Society of London, 174:935–982, 1883.
[531] W. Rippl. The Capacity of Storage Reservoirs for Water Supply. Proceedings of the Institution
of Civil Engineers, London, 71:270, 1883.
[532] J.A. Roberson and C.T. Crowe. Engineering Fluid Mechanics. John Wiley Sons, New
York, New York, sixth edition, 1997.
[533] F. Rodriguez, H. Andrieu, and J.-D. Creutin. Surface runoff in urban catchments: mor-
phological identification of unit hydrographs from urban databanks. Journal of Hydrology,
283:146–168, 2003.

[534] M.I. Rorabaugh. Graphical and theoretical analysis of step-drawdown test of artsian well.
Proceedings of the American Society of Civil Enginers, 79(362):23 pp., 1953.
[535] Roscoe Moss Company. Handbook of Groundwater Development. John Wiley Sons, New
[536] J.R. Rossing. Identification of critical runoff generating areas using a variable source area
model. PhD thesis, Cornell University, Ithaca, New York, 1996.
[537] L.A. Rossman. Computer models/epanet. In L.W. Mays, editor, Water Distribution Systems
Handbook, pages 12.1–12.23. McGraw-Hill Book Company, New York, New York, 2000.
[538] W.M. Grayman L.A. Rossman and E.E. Geldreich. Water quality. In L.W. Mays, editor,
Water Distribution Systems Handbook, pages 9.1–9.24. McGraw-Hill Book Company, New
[539] R.L. Rossmiller. The rational formula revisited. In Proceedings of the International Sympo-
sium on Urban Storm Runoff, July 28-31, Lexington, Kentucky, 1980. University of Kentucky.
[540] J. Rothacher. Net precipitation under a Douglas-fir forest. Forest Science, 9(4):423–429,
1963.
[541] H. Rouse. Elementary Fluid Mechanics. John Wiley Sons, New York, New York, 1946.
[542] H. Rouse and S. Ince. History of Hydraulics. Iowa Institute of Hydraulic Research, University
of Iowa, Iowa City, 1957.
[543] L.K. Rowe. Rainfall interception by a beech-podocarp-hardwood forest near Reefton, North
Westland, New Zealand. Journal of Hydrology (N.Z.), 18(2):63–72, 1979.
[544] H. Rubin and J. Atkinson. Environmental Fluid Mechanics. Marcel Dekker, Inc., New York,
New York, 2001.
[545] M.L. Sage and G.W. Sage. Vapor Pressure. In R.S. Boethling and D. Mackay, editors,
Handbook of Property Estimation Methods for Chemicals, pages 53–65. Lewis Publishers,
Inc., Boca Raton, Florida, 2000.
[546] J.D. Salas. Analysis and modeling of hydrologic time series. In D.R. Maidment, editor,
Handbook of Hydrology, pages 19.1–19.72. McGraw-Hill Book Company, New York, New
York, 1993.
[547] G.D. Salvucci and D. Entekhabi. Explicit expressions for Green-Ampt (delta function diffu-
sivity) infiltration rate and cumulative storage. Water Resources Research, 30(9):2661–2663,
September 1994.
[548] Z. Samani. Estimating solar radiation and evapotranspiration using minimum climatological
data. Journal of Irrigation and Drainage Engineering, ASCE, 126(4):265–267, 2000.
[549] X. Sánchez-Vila, P.M. Meier, and J. Carrera. Pumping tests in heterogeneous aquifers: An
analytical study of what can be obtained from their interpretation using Jacob’s method.
Water Resources Research, 35(4):943–952, April 1999.

840
[550] R. Schildgen. Unnatural disasters. Sierra, 84:48–57, 1999.
[551] H. Schlichting. Boundary Layer Theory. McGraw-Hill, Inc., New York, New York, seventh
edition, 1979.
[552] S. Schmorak and A. Mercado. Upconing of fresh water-sea water interface below pumping
wells, field study. Water Resources Research, 5:1290–1311, 1969.
[553] J.L. Schnoor. Environmental Modeling: Fate and Transport of Pollutants in Water, Air, and
Soil. John Wiley Sons, New York, New York, 1996.
[554] T.R. Schueler. Controlling urban runoff: A practical manual for planning and designing urban
BMPs. Metropolitan Washington Council of Governments, Washington, DC, 1987.
[555] T.R. Schueler, P.A. Crumble, and M.A. Heraty. Current Assessment of Urban Best Manage-
ment Practices: Techniques for Reducing Non-point Source Pollution in the Coastal Zones.
Metropolitan Washington Council of Governments, Washington, DC, 1991.
[556] C.K. Sehgal. Design guidelines for spillway gates. Journal of Hydraulic Engineering,
122(3):155–165, March 1996.
[557] Soil Conservation Service. SCS National Engineering Handbook, Section 4: Hydrology. U.S.
Department of Agriculture, Washinton, DC, 1993.
[558] R.M. Shane and W.R. Lynn. Mathematical model for flood risk evaluation. Journal of the
Hydraulics Division, ASCE, 90(HY6):1–20, November 1964.
[559] L.K. Sherman. Stream-flow from rainfall by the unit graph method. Engineering News Record,
108:501–505, 1932.
[560] J.-T. Shiau and H.W. Shen. Recurrence analysis of hydrologic droughts of differing severity.
Journal of Water Resources Planning and Management, 127(1):30–40, January/February
2001.
[561] V. Sichard. Das Fassungsvermögen von Bohrbrunnen und Eine Bedeutung für die Grund-
wasserersenkung inbesondere für grossere Absentiefen. PhD thesis, Tech. Hochschule, Berlin,
1927.
[562] J.R. Simanton and H.B. Osborn. Reciprocal-distance estimate of point rainfall. Journal of
the Hydraulic Engineering Division, ASCE, 106(HY7), July 1980.
[563] D.B. Simons and E.V. Richardson. Resistance to Flow in Alluvial Channels. Professional
Paper 422-J, U.S. Geological Survey, Washington, DC, 1966.
[564] V.P. Singh. Hydrologic Systems, Rainfall-Runoff Modeling, Volume I. Prentice-Hall, Engle-
wood Cliffs, New Jersey, 1989.
[565] V.P. Singh. Elementary Hydrology. Prentice-Hall, Upper Saddle River, New Jersey, 1992.
[566] V.P. Singh and W.G. Strupczewski. On the status of flood frequency analysis. Hydrological
Processes, 16:3737–3740, 2002b.

[567] M.K. Smith. Throughfall, stemflow, and interception in pine and eucalypt forests. Australian
Forestry, 36:190–197, 1974.
[568] M.R. Smith, R.G. Allen, J.L. Monteith, L.S. Pereira, and A. Segeren. Report on the Expert
Consultation on Procedures for Revision of FAO Guidelines for Predicting Crop Water Re-
quirements. Technical report, Land and Water Development Division, Food and Agricultural
Organization of the United Nations, Rome, 1991.
[569] R.E. Smith. Discussion of ‘Runoff curve number: Has it reached maturity?’ by V.M. Ponce
and R.H. Hawkins. Journal of Hydrologic Engineering, 2(3):145–147, 1997.
[570] F.F Snyder. Synthetic Unit Hydrographs. Transactions of the American Geophysical Union,
19:447, 1938.
[571] Soil Conservation Service. Computer program for project formulation hydrology (draft).
Technical Release 20, Soil Conservation Service, U.S. Department of Agriculture, Washington,
DC, 1983.
[572] Soil Conservation Service. Urban hydrology for small watersheds. Technical Release 55, Soil
Conservation Service, U.S. Department of Agriculture, Washington, DC, 1986.
[573] W.B. Solley. Estimated Use of Water in the United States in 1995. Circular 1200, U.S.
Geological Survey, Washington, DC, 1998.
[574] South Carolina Land Resources Conservation Commission. South Carolina stormwater man-
agement and sediment reduction regulations. Technical report, Division of Engineering,
Columbia, South Carolina, 1992.
[575] South Florida Water Management District. Management and Storage of Surface Waters,
Permit Information Manual, Volume IV. West Palm Beach, Florida, May 1994.
[576] South Florida Water Management District. Best Management Practices for South Florida
Urban Stormwater Management Systems. West Palm Beach, Florida, April 2002.
[577] M.S. Sperry and J.J. Pierce. A model for estimating the hydraulic conductivity of granu-
lar material based on grain shape, grain size, and porosity. Ground Water, 33(6):892–898,
November-December 1995.
[578] P. Stahre and B. Urbonas. Swedish approach to infiltration and percolation design. In L.A.
Roesner, B. Urbonas, and M.B. Sonnen, editors, Design of Urban Runoff Quality Controls,
pages 307–323. ASCE, New York, New York, 1989.
[579] R.W. Stallman. Aquifer-test design, observation and data analysis. Techniques of Water
Resources Investigations, Book 3, Chapter B1, U.S. Geological Survey, 1971.
[580] G. Stanhill. The control of field irrigation practice from measurements of evaporation. Israel
J. Agric. Res., 12:51–62, 1962.
[581] T.E. Stanton and J.R. Pannell. Similarity of motion in relation to surface friction of fluids.
Philosophical Transactions, Royal Society of London, 214A:199–224, 1914.

842
[582] A.J. Stepanoﬀ. Centrifugal and Axial Flow Pumps. John Wiley Sons, New York, New
York, second edition, 1957.
[583] W.J. Stone. Hydrogeology in Practice. Prentice-Hall, Upper Saddle River, New Jersey, 1999.
[584] R.L. Street, G.Z. Watters, and J.K. Vennard. Elementary Fluid Mechanics. John Wiley
Sons, New York, New York, seventh edition, 1996.
[585] V.L. Streeter and E.B. Wylie. Fluid Mechanics. McGraw-Hill, Inc., New York, New York,
eighth edition, 1985.
[586] V.L. Streeter, E.B. Wylie, and K.W. Bedford. Fluid Mechanics. McGraw-Hill, Inc., New
York, New York, ninth edition, 1998.
[587] A. Strickler. Contributions to the question of a velocity formula and roughness data for
streams, channels and closed pipelines. Technical report, W.M. Keck Laboratory, California
Institute of Technology, Pasadena, California, 1923. Translation by T. Roesgen and W.R.
Brownlie (1981).
[588] W.G. Strupczewski, V.P. Singh, and S. Weglarczyk. Asymptotic bias of estimation methods
caused by the assumption of false probability distribution. Journal of Hydrology, 258:122–148,
2002.
[589] J.M. Stubchaer. The Santa Barbara Urban Hydrograph Method. Proceedings, National Sym-
posium of Hydrology and Sediment Control, University of Kentucky, Lexington, Kentucky,
1980.
[590] T. Sturm. Open Channel Hydraulics. McGraw-Hill, Inc., New York, New York, 2001.
[591] P.K. Swamee. Generalized rectangular weir equations. Journal of Hydraulic Engineering,
114(8):945–949, 1988.
[592] P.K. Swamee and A.K. Jain. Explicit Equations for Pipe-Flow Problems. ASCE, Journal of
the Hydraulics Division, 102(HY5):657–664, May 1976.
[593] W.T. Swank, N.B. Goebel, and J.D. Helvey. Interception loss in loblolly pine stands in the
piedmont of South Carolina. Journal of Soil and Water Conservation, 27(4):160–164, 1972.
[594] R.M. Sykes. Water and Wastewater Planning. In W.F. Chen, editor, The Civil Engineering
Handbook, pages 169–223. CRC Press, Inc., Boca Raton, Florida, 1995.
[595] T. Szirtes. Applied Dimensional Analysis and Modeling. McGraw-Hill, Inc., New York, New
York, 1998.
[596] L.M. Tallaksen. A Review of Baseﬂow Recession Analysis. Journal of Hydrology, 165, 1995.
[597] G.D. Tasker and J.R. Stedinger. Regional skew with weighted LS regression. Journal of
Water Resources Planning and Management, 112(2):225–237, April 1986.
[598] B.N. Taylor. Guide for the use of the international system of units (si). Technical report,
National Institute of Standards and Technology, 1995. NIST Special Publication 811, 1995
Edition.

[599] D.W. Taylor. Fundamentals of Soil Mechanics. Wiley, New York, New York, 1948.
[600] C.V. Theis. The relation between lowering of the piezometric surface and the rate and
duration of discharge of a well using ground water storage. In Transactions of the American
Geophysical Union, 16th Annual Meeting, Part 2, pages 519–524, 1935.
[601] H.J. Thiébaux. Statistical Data Analysis for Ocean and Atmospheric Sciences. Academic
Press, Inc., San Diego, California, 1994.
[602] G. Thiem. Hydrologische. Gebhardt, Leipzig, Germany, 1906.
[603] A.H. Thiessen. Precipitation for large areas. Monthly Weather Review, 39:1082–1084, July
1911.
[604] A.L. Tholin and C.J. Keifer. The hydrology of urban runoff. Transactions of the American
Society of Civil Engineers, 125:1308, 1960.
[605] A.S. Thom and H.R. Oliver. On Penman’s equation for estimating regional evapotranspira-
tion. Quarterly Journal of Royal Meteorological Society, 103:345–357, 1977.
[606] G.W. Thomas and R.E. Phillips. Consequences of water movement in macropores. J. Environ.
Qual., 8(2):149–152, 1979.
[607] L. Thomas. What Causes Wells to Lose Capacity? Opflow, 28(1):8–15, January 2002.
American Water Works Association.
[608] C.W. Thornthwaite. An approach toward a rational classification of climate. Geograph. Rev,
38:55, 1948.
[609] C.W. Thornthwaite and J.R. Mather. The water balance. Climatology, 8(1), 1955. Lab. of
Climat., Centeron, N.J.
[610] J.A. Tindall and J.R. Kunkel. Unsaturated Zone Hydrology for Scientists and Engineers.
Prentice-Hall, Upper Saddle River, New Jersey, 1999.
[611] D.K. Todd. Groundwater Hydrology. John Wiley Sons, New York, New York, second
edition, 1980.
[612] M. Todorovic. Single-layer evapotranspiration model with variable canopy resistance. Journal
of Irrigation and Drainage Engineering, ASCE, 125(5):235–245, 1999.
[613] P.A. Troch, F.P. De Troch, and W. Brutsaert. Effective water table depth to describe initial
conditions prior to storm rainfall in humid regions. Water Resources Research, 29(2):427–434,
1993.
[614] I.K. Tuncock and L.W. Mays. Hydraulic design of culverts and highway structures. In L.W.
Mays, editor, Hydraulic Design Handbook, pages 15.1–15.71. McGraw-Hill Book Company,

844
[615] L. Turc. Evaluation des besoins en eau d’irrigation, evapotranspiration potentielle, formule
climatique simplifice et mise a jour (in French). (English title: Estimation of irrigation water
requirements, potential evapotranspiration: A simple climatic formula evolved up to date).
Ann. Agron., 12:13–49, 1961.
[616] G.J.G. Upton and A.R. Rahimi. On-line detection of errors in tipping-bucket raingages.
Journal of Hydrology, 278:197–212, 2003.
[617] Urban Drainage and Flood Control District. Urban Storm Drainage Criteria Manual. Denver
Regional Council of Governments, Denver, Colorado, 1984.
[618] B. Urbonas and P. Stahre. Stormwater: Best Management Practices and Detention for Water
Quality, Drainage, and CSO Management. Prentice-Hall, Upper Saddle River, New Jersey,
1993.
[619] B.R. Urbonas and L.A. Roesner. Hydrologic Design for Urban Drainage and Flood Control.
In D.R. Maidment, editor, Handbook of Hydrology, page Chapter 28. McGraw-Hill, Inc., New
[620] U.S. Army Corps of Engineers. Standard Project Flood Determination. Report EM 1110-2-
1411, U.S. Army Corps of Engineers, Washington, DC, March 1965.
[621] U.S. Army Corps of Engineers. Feasibility Studies for Small Scale Hydropower Additions,
Volume 3. Hydrologic Engineering Center, Davis, California, 1979.
[622] U.S. Army Corps of Engineers. Reservoir system analysis for conservation, HEC-3. Hydro-
logic Engineering Center, Davis, California, 1981.
[623] U.S. Army Corps of Engineers. Simulation of flood control and conservation systems, HEC-5.
Hydrologic Engineering Center, Davis, California, 1982.
[624] U.S. Army Corps of Engineers. Hydropower engineering manual. Report EM-1110-2-1701,
Engineering Design, U.S. Army Corps of Engineers, Washington, DC, 1985.
[625] U.S. Army Corps of Engineers. Accuracy of Computed Water Water Surface Profiles. Hy-
drologic Engineering Center, Davis, California, 1986.
[626] U.S. Army Corps of Engineers. Digest of water resources policies and authorities. Report EP
1165-2-1, U.S. Army Corps of Engineers, Washington, DC, 1989.
[627] U.S. Army Corps of Engineers. Interior Flood Hydrology package, HEC-IFH. Hydrologic
Engineering Center, Davis, California, 1992.
[628] U.S. Army Corps of Engineers. Hydrologic Frequency Analysis. Report EM 1110-2-1415,
U.S. Army Corps of Engineers, Washington, DC, 1993.
[629] U.S. Army Corps of Engineers. Hydraulic design of flood control channels. Report EM
1110-2-1601, U.S. Army Corps of Engineers, Washington, DC, 1994.
[630] U.S. Army Corps of Engineers. Hydraulic Design of Flood Control Channels. American
Society of Civil Engineers, New York, New York, 1995.

Water-Resources-Engineering-Chin.pdf

More Related Content

What's hot (20)

Similar to Water-Resources-Engineering-Chin.pdf (20)

Recently uploaded (20)

Water-Resources-Engineering-Chin.pdf