Womersley number

The Womersley number (${\displaystyle \alpha }$ or ${\displaystyle {\text{Wo}}}$) is a dimensionless number in biofluid mechanics and biofluid dynamics. 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 blood flow 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.

The square of this number is also referred to as the Stokes number, ${\displaystyle {\text{Stk}}={\text{Wo}}^{2}}$, due to the pioneering work done by Sir George Stokes on the Stokes second problem.