Numbers

ARCHIMEDES NUMBER is proportional to { (gravitational force) / (viscous force) } and is used in momentum transfer in general and buoyancy, fluidization, and motion due to density

difference calculations in particular. It is normally defined in the following form :

Where:

g = Gravitational acceleration

L = Characteristic length

mu = Viscosity

rho_f = Fluid density

rho_s = Solid density

Arrhenius number is proportional to { (activation energy) / (potential energy) } and is used in

mass transfer in general and reaction rate calculations in particular. It is normally defined in the

following form

Where:

Eo = Activation Energy

R = Gas law constant

T = Temperature

Bingham number is proportional to { (yield stress) / (viscous stress) } and is used in momentum

transfer in general and flow of bingham plastics calculations in particular. It is normally defined

in the following form :

Where:

gc = Dimensional constant


mu = Viscosity

tau_y = Stress

V = Velocity

Biot number is proportional to { (thermal internal resistance) / (surface film resistance) } and is

used in heat transfer in general and unsteady state calculations in particular. It is normally

defined in the following form :

Where:

delta-x = Mid-plane distance

h_T = Heat transfer coefficient

k = Thermal Conductivity

Blake number is proportional to { (inertial force) / (viscous force) } and is used in momentum

transfer in general and flow through beds of solids calculations in particular. It is normally

defined in one of the following forms :

or

Where:

epsilon = Void fraction

G = Mass velocity

mu = Viscosity

rho = Density

s = Particle area/particle volume

V = Velocity

Bodenstein number is used in mass transfer in general and diffusion in reactors calculations in

particular. It is normally defined in the following form :

Where:

Dv,a = Effective axial diffusivity

L = Reactor length

V = Velocity

Where:

d = Droplet/bubble diameter



rho = Droplet/bubble density

rho_f = Surrounding fluid density

sigma = Surface tension

Capillary number is proportional to { (viscous force) / (surface tension force) } and is used in

momentum transfer in general and atomization and 2-phase flow in beds of solids calculations in

particular. It is equivalent to (We/Re). It is normally defined in the following form

Where:


mu = Viscosity


V = Velocity

Cauchy number is proportional to { (inertial force) / (compressibility force) } and is used in

momentum transfer in general and compressible flow calculations in particular. It is normally


Where:

Eb = bulk modulus of fluid


rho = Density

V = Velocity

Cavitation number is proportional to { (excess of local static head over vapor pressure head) /

(velocity head) } and is used in momentum transfer in general and throttling calculations in


Where:


p = Local static pressure

p_v = Vapor pressure

rho = Density

V = Velocity

Colburn-Chilton j factor is used in heat transfer in general and free and forced convection

calculations in particular. It is equivalent to (St.Pr^2/3). It is normally defined in one of the

following forms :

or

Where:

Cp = Heat capacity

G = Mass velocity

h = Heat transfer coefficient


mu = Viscosity

rho = Density

V = Velocity

Condensation number is used in heat transfer in general and as the name implies in condensation

calculations in particular. It is normally defined in one of the following forms :

or

Where:

delta-T = Temperature difference

lambda = Latent heat

g = Gravitational

acceleration




mu = Viscosity

rho = Density

Drag Coefficient

Drag coefficient is proportional to { (gravitational force) / (inertial force) } and is used in

momentum transfer in general and free settling velocities and resistance to flow calculations in


Where:


L = Characteristic dimension of object

rho = Density of object

rho_f = Density of surrounding fluid

V = Velocity

Eckert Number

Eckert number is used in momentum and heat transfer in general and compressible flow

calculations in particular. It is normally defined in the following form :

Where:

Cp = Heat capacity


V_inf = Velocity of fluid far from body

Elasticity Number

Elasticity number is proportional to { (elastic force) / (inertial force) } and is used in momentum

transfer in general and viscoelastic flow calculations in particular. It is normally defined in the

following form :

Where:

r = Pipe/conduit radius

mu = Viscosity

rho = Density

theta = relaxation time

Etvs number is proportional to { (gravitational force) / (surface tension force) } and is used in

momentum transfer in general and atomization, and motion of bubbles and droplets calculations

in particular. It is equivalent to (Bo). It is normally defined in the following form :

Where:


rho = Density of

bubble/droplet

rho_f = Density of surrounding fluid


Euler Number

Euler number is proportional to { (friction head) * (velocity head) } and is used in momentum

transfer in general and fluid friction in conduits calculations in particular. It is equivalent to (N/2)

where N is the number of velocity heads. It is normally defined in one of the following forms :

or

Where:

delta-P = Pressure drop


G = Mass velocity

rho = Density

V = Velocity

Fourier Number

Fourier number is used in heat transfer in general and unsteady state heat transfer calculations in

particular. It is normally defined in one of the following forms :

or

Where:

alpha = Thermal diffusivity

Cp = Heat capacity



rho = Density

t = Time

Froude Number

Froude number is proportional to { (inertial force) / (gravitational force) } and is used in

momentum transfer in general and open channel flow and wave and surface behavior

calculations in particular. It is normally defined in one of the following forms

or

Where:

a = Acceleration



V = Velocity

Galileo Number

Galileo number is proportional to { (Re. gravity force) / (viscous force) } and is used in

momentum and heat transfer in general and viscous flow and thermal expansion calculations in


Where:


D = Diameter

mu = Viscosity

rho = Density

Grtz Number

Grtz number is proportional to { (thermal capacity) / (convective heat transfer) } and is used in

heat transfer in general and convection in laminar flow calculations in particular. It is equivalent

to {(L/d) / (Re.Pr)} or {(L/d) / Pe}. It is normally defined in one of the following forms :

Where:


Cp = Heat capacity

d = Diameter

G = Mass velocity


L = Length

m = Mass flowrate

rho = Density

V = Velocity

Grashof Number

Grashof number is proportional to { (buoyancy force) / (viscous force) } and is used in heat

transfer in general and free convection calculations in particular. It is normally defined in one of

the following forms :

or

Where:

beta = Coefficient of expansion


G = Gravitational acceleration


mu = Viscosity

V = Kinematic viscosity

rho = Density

Hodgson Number

Hodgson number is proportional to { (time constant of system) / (period of pulsation) } and is

used in momentum transfer in general and unsteady pulsating gas flow calculations in particular.

It is normally defined in the following form :

Where:

delta-P = Pressure drop

fr = Frequency

p = Avg. static pressure

q = Avg. volumetric flowrate

V = System Volume

Knudsen Number

Knudsen number is proportional to { (length of mean free path) / (characteristic dimension) }

and is used in momentum and mass transfer in general and very low pressure gas flow


Where:

lambda = Length of mean free path

L = Characteristic dimension

Lewis Number

Lewis number is used in combined heat and mass transfer calculations. It is equivalent to (Sc/Pr).

It is normally defined in one of the following forms :

or

Where:


Cp = Heat capacity

Dv = Diffusivity


rho = Density

Mach number is used in momentum transfer in general and near/ultra sonic flow and throttling


Where:

V = Velocity

V_sound = Velocity of sound in fluid

Nusselt Number

Nusselt number is proportional to { (total heat transfer) / (conductive heat transfer) } and is used

in heat transfer in general and forced convection calculations in particular. It is normally defined

in the following form :

Where:


D = Diameter


Ohnesorge Number

Ohnesorge number is proportional to { (viscous force) / (sqrt (inertial force . surface tension

force)) } and is used in momentum transfer in general and atomization calculations in particular.

It is equivalent to (SQRT(We) / Re). It is normally defined in the following form :

Where:



mu = Viscosity

rho = Density


Peclet Number

Peclet number is proportional to { (bulk heat transfer) / (conductive heat transfer) } and is used

in heat transfer in general and forced convection calculations in particular. It is equivalent to

(Re.Pr). It is normally defined in one of the following forms :

or

Where:


Cp = Heat capacity

D = Characteristic length

G = Mass velocity


rho = Density

V = Velocity

Pipeline Parameter

Pipeline parameter is proportional to { (maximum water-hammer pressure rise) / (2 static

pressure) } and is used in momentum transfer in general and hydraulic transients calculations in


Where:

a = Wave velocity


H = Static head

Vo = Initial velocity

Power Number

Power number is proportional to { (drag force) / (inertial force) } and is used in momentum

transfer in general and power consumption by agitators, fans, pumps, etc. calculations in


Where:



N = Rate of rotation

P = Power

rho = Density

Prandtl Number

Prandtl number is proportional to { (momentum diffusivity) / (thermal diffusivity) } and is used

in heat transfer in general and free and forced convection calculations in particular. It is normally


Where:

Cp = Heat capacity


mu = Viscosity

Rayleigh Number

Rayleigh number is used in heat transfer in general and free convection calculations in particular.

It is equivalent to (Gr.Pr). It is normally defined in one of the following forms :

or

Where:


beta = Coefficient of expansion

Cp = Heat capacity





mu = Viscosity

rho = Density

Reynolds Number

Reynolds number is proportional to { (inertial force) / (viscous force) } and is used in

momentum, heat, and mass transfer to account for dynamic similarity. It is normally defined in

one of the following forms

For Reynolds Number Calculation using the above formula please go Here

http://www.processassociates.com/reynolds.php

or

Where:


G = Mass velocity

mu = Viscosity

rho = Density

V = Velocity

Schmidt Number

Schmidt number is proportional to { (kinetic viscosity) / (molecular diffusivity) } and is used in

mass transfer in general and diffusion in flowing systems calculations in particular. It is normally


Where:

Dv = Diffusivity

mu = Viscosity

rho = Density

Sherwood Number

Sherwood number is proportional to { (massr diffusivity) / (molecular diffusivity) } and is used

in mass transfer calculations. It is equivalent to (jm.Re.Sc1/3). It is normally defined in the

following form :

Where:

Dv = Diffusivity

kc = Diffusion rate


Stanton Number

Stanton number is proportional to { (heat transfered) / (thermal capacity of fluid) } and is used in

heat transfer in general and forced convection calculations in particular. It is equivalent to (Nu /

(Re.Pr)). It is normally defined in one of the following forms :

or

Where:

Cp = Heat capacity

G = Mass velocity


rho = Density

V = Velocity

Strouhal Number

Strouhal number is proportional to the reciprocal of vortex spacing expressed as no. of obstacle

diameters and is used in momentum transfer in general and Van Karman vortex streets and

unsteady state flow calculations in particular. It is normally defined in the following form :

Where:

fr = frequency


V = Velocity

Weber Number

Weber number is proportional to { (inertial force) / (surface tension force) } and is used in

momentum transfer in general and bubble/droplet formation and breakage of liquid jets

calculations in particular. It is normally defined in one of the following forms :

or

Where:


G = Mass velocity


rho = Density


V = Velocity

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