# The Wormersley Number a a Frequency Parameter for Pulsatile Flow

The Wormersley number, or alpha parameter, is another dimensionless parameter that is used in the study of fluid mechanics. This parameter represents a ratio of transient to viscous forces, just as the Reynolds number represented a ratio of inertial to viscous forces. A characteristic frequency represents the time dependence of the parameter. The Wormersley number may be written by:

 p = the vessel radius v = the fundamental frequency p = the density of the fluid m = the viscosity of the fluid n = the kinematic viscosity

In higher frequency flows, the flow profile is blunter near the centerline of the vessel since inertia becomes more important than viscous forces. Near the wall, where V is close to zero, viscous forces are still important.

Some typical values of the a parameter for various species are as follows:

 (#) a = 20 (#) a = 14 (#) a = 8 (#) a 3The fundamental frequency is typically the heart rate. The units must be rad/s for dimensional consistency. This page intentionally left blank Chapter 2