# Womersley Number

## Description

The Womersley number (α) is a dimensionless number in biofluid mechanics. It is a dimensionless expression of the pulsatile flow frequency in relation to viscous effects. It is named after John R. Womersley (1907–1958) for his work with bloodflow in arteries. The Womersley number is important in keeping dynamic similarity when scaling an experiment. An example of this is scaling up the vascular system for experimental study. The Womersley number is also important in determining the thickness of the boundary layer to see if entrance effects can be ignored.

Related formulas## Variables

a | Womersley number (dimensionless) |

R | appropriate length scale (for example the radius of a pipe) (m) |

ω | angular frequency of the oscillation (1/s) |

ρ | density (kg/m^{3}) |

μ | dynamic viscosity of the fluid (pascal*s) |