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 |

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