Dimensionless number

ANWESA KAR
M.TECH(THERMAL ENGG.)

1.REYNOLDS NUMBER
 It is the ratio of inertia force to the viscous force.
Where,
Re
VL


 is density
is velocity
L is linear dimension
 is viscosity
Significance-It is used to identify the nature of
flow (Laminar or Turbulent)
V

2.FROUDE NUMBER
 It is the ratio of inertia force to the gravity force
 Where ,
V is the velocity
g is the acceleration due to gravity
L is the characteristics length
Significance-It is used to analyze nature of flow where
free surface is present. e.g. weirs ,channels ,spillways
V
Fr
gL


3.WEBERS NUMBER
 It is the ratio of inertia force to surface tension force.
 Where
V is the velocity
Significance-It is used in analyzing formation of droplet
and in capillary studies.
/
V
We
L 

 is the surface tension
 is the density

4.EULER NUMBER
 It is the ratio of inertia force to pressure force.
 Where
P is the pressure
V is the velocity
Significance-It is used to characterize energy losses in a
flow.
V
Eu
P


 is the density

5.MACH NUMBER
 It is the ratio of inertia force to elastic force.
 Where
V is the velocity of object
C is the speed of sound
Significance-It is used to analyze fluid flow where
compressibility is a important factor.
V
M
C


6.BIOT NUMBER
 It is the ratio of conductive resistance to convective
resistance.
Where
h is the heat transfer coefficient
K is the thermal conductivity
Significance-It is used in the heat transfer calculation
(lumped heat analysis).
chL
Bi
K

cL is the characteristics length(volume of
the body/surface area of contact)

7.FOURIER NUMBER
 It is the ratio of heat conducted through a body to the
heat stored.
 Where,
t is the characteristics time
 Significance-It is used in transient heat analysis.
2
c
t
L

 
 is the thermal diffusivity
cL is the length

8.NUSSELT NUMBER
It is the ratio of convective heat transfer to conductive heat
transfer.
Where
h is the convective heat transfer coefficient
Significance-It describe the enhancement of heat transfer
because of convection in comparison to conduction
hL
Nu
K


9.PRANDTL NUMBER
 It is the ratio of momentum diffusivity to heat diffusivity
 Where
Significance-Prandtl number is used to describe thermal
boundary layer.
Pr PC
K


 is the dynamic viscosity
PC is the specific heat

10.GRASHOF NUMBER
 It is the ratio of buoyancy force to viscous force.
 Where
g is acceleration due to gravity
Significance-It is used in flow analysis in natural convection.
 is the coefficient of thermal expansion
sT is the surface temperature
T is the fluid temperature far from the surface
 is the kinematic viscosity of fluid
3
2
( )s cg T T L
Gr





11.RAYLEIGH NUMBER
 Rayleigh number is the product of Grashof number
and Prandtl number.
Ra= Gr . Pr
Significance-It is associated with buoyancy driven flow .
Its value is used to characterize laminar to turbulent
transition.

12.STANTON NUMBER
 It is defined as the ratio of heat transferred by convection
to the heat capacity of fluid.
 Where h is the heat transfer coefficient
u is the speed of fluid
Significance-It is used in heat transfer for forced
convection flows.
Re.Pr p
Nu h
St
uC
 
 is the density of fluid
pC is the Specific heat capacity of the fluid

13.PECLET NUMBER
 It is defined as the product of Reynold number and
Prandtl number.
 Where
u is the velocity
Significance-It is used in calculations including
convective heat transfer rate.
Re.Pr
Lu
Pe

 

14.JAKOB NUMBER
 It is the ratio of sensible energy absorbed to latent
energy absorbed during liquid- vapor phase change.
 Where
Significance-It is used in analyzing flow pattern in
process of boiling.
( )P s sat
fg
C T T
Ja
h


PC
s satT T
fgh
is the specific heat capacity
is the temperature difference
Latent heat of vaporization

15.BOND NUMBER
 It is the ratio of buoyancy force to the surface tension
force.
 Where
g is the acceleration due to gravity
Significance-It is used in analyzing the behavior of
bubbles.
1 2( )g
Bo
 



1 2( )  is the difference in density
 is the surface tension

16.SCHIMDT NUMBER
 It is the ratio of momentum diffusivity to mass
diffusivity.
 Where
D is the mass diffusivity
Significance-It is used in fluid flows where simultaneous
mass and momentum diffusion occurs.
Sc
D


 is the kinematic viscosity

17.LEWIS NUMBER
 It is the ratio of thermal diffusivity to the mass diffusivity.
Where
Significance-It is used to analyze fluid flow with
simultaneous heat and mass transfer by convection.
p
K
Le
D C D


 
pC is the specific heat capacity

18.SOMMERFELD NUMBER
 Sommerfeld number is defined by the following equation
Where
r is the radius of the journal
c is the radial clearance
P is the bearing pressure
Significance-It is used in hydrodynamic lubrication
analysis.
2
. snr
S
c P
 
  
 
 is the dynamic viscosity
sn is the journal speed in r.p.s

19.KNUDSEN NUMBER
 It is the ratio of molecular mean free path to the
characteristics length.
 Where
Significance-It is useful in determining whether
continuum mechanics formulation can be applied or
not in a system.
Kn
L


 is the mean free path

20.SHERWOOD NUMBER
 It is the ratio of convection mass transfer to the
diffusion mass transfer
 Where
K is the mass transfer coefficient
l is the characteristics length
Significance-It is used in mass transfer problems.
Kl
Sh
D


Dimensionless number

More Related Content

What's hot

Similar to Dimensionless number

Recently uploaded

In this document

Dimensionless number