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.

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Chapter 2

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