# Womersley Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Womersley number, abbreviated as a, a dimensionless number, is the pulsatile flow frequency in relation to viscous effects.

### Womersley Number Formula

$$\large{ a = l \; \sqrt{ \frac{ \omega \; \rho }{ \mu } } }$$

Where:

$$\large{ a }$$ = Womersley number

$$\large{ l }$$ = approperate length scale (for example the radius of a pipe)

$$\large{ \omega }$$  (Greek symbol omega) = angular frequency of the oscillation

$$\large{ \rho }$$   (Greek symbol rho) = density

$$\large{ \mu }$$  (Greek symbol mu) = fluid dynamic viscosity