Fluid Dynamics Dimensionless Numbers - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 349

Name Symbol Equation Description

ϑ
α

Prandtl number Pr Defined as the ratio of momentum diffusivity

(kinematic viscosity) to thermal diffusivity

VL
ϑ

Reynolds number Re Defined as the ratio of a characteristic velocity to a

characteristic length. Used to determine the flow
regime (laminar or turbulent)

ϑ
D ab

Schmidt number Sc Defined as the ratio of momentum diffusivity and

mass diffusivity

τV
L C

Stokes number Stk Defined as the ratio of the stopping distance of a

particle to a characteristic dimension of the
obstacle

ωL
V

Strouhal number St Defined as the ratio of the oscillations in a flow to

the fluid inertia. Used to describe oscillating flow

ρV 2 L
σ

Weber number We Defined as the ratio of a fluid's inertia compared to

its surface tension

ω
ϑ

0 . 5

L
2

Womersley
number

α Defined as the ratio of the pulsatile flow frequency to

viscous effects

C.1 Nomenclature

a speed of sound

D ab mass diffusivity

D

diffusion coefficient

g gravitational acceleration

h heat transfer coefficient

h m mass transfer coefficient

k thermal conductivity of the body

L C characteristic length, which is commonly defined as the volume of the body

divided y the surface area of the body, L C = V body /A surface

L representative physical length scale

V velocity

T temperature difference

α =

α thermal diffusivity, k/ ( ρ C p ) where C p is the specific heat capacity

β volumetric thermal expansion coefficient equal to the inverse of the film

temperature

λ mean free path

ρ fluid density

σ surface tension

relaxation time of a particle defined as ρ p d p 2 / 18 μ , where subscripts p , denote
particle, and d p is the particle diameter

τ

ϑ kinematic viscosity

ω oscillation frequency, or breathing frequency