Fluid Dynamics Dimensionless Numbers - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 348

Appendix C
Fluid Dynamics Dimensionless Numbers

Name Symbol Equation Description

hL C
k

Biot number Bi Defined as the ratio of the heat transfer

resistances inside of and at the surface of an
object

h m L C
D ab

Biot number
(mass transfer)

Bi mass Defined as the ratio between the the mass transfer

rate to t the mass diffusion rate of an object

Re L
2 R

1 / 2

Dean number De Defined as the product of the Reynolds number

(based on axial flow V through a pipe of
diameter L) and the square root of the
curvature ratio

V
( gL C ) 2

Froude number Fr Defined as the ratio of the inertia force on a body

to the weight of the body—the inertial force
divided by gravitational force

gβT V
ϑ 2

Grashof number Gr Defined as the ratio of the buoyancy force to

viscous force acting on a fluid. Often used
when natural convection is important

λ
L

Knudsen number Kn Defined as the ratio of the molecular mean free

path length to a representative physical length
scale

α
D ab

Lewis number Le Defined as the ratio of thermal diffusivity to mass

diffusivity

V
a

Mach number Ma A measure of velocity relative to the speed of

sound, e.g. 1 Mach = 343 m/s in dry air at
20 ◦ C (68 ◦ F)

hL C
k

Nusselt number Nu Defined as the ratio of convective to conductive

heat transfer across (normal to) the boundary

√ We
Re

Ohnesorge
number

Oh Defined as the ratio of the viscous forces to

inertial and surface tension forces

VL
D

Peclet number Pe Defined as the ratio of advection (convection) to

the rate of diffusion