Pulsatile flow in rigid tubes

Abstract

The purpose of this study was to examine critically the theoretical equations derived for pulsatile laminar flow in rigid straight tubes. These equations, presented in their most useful form by J. R. Womersley in 1955, give the fluid flow rate as a function of the pressure gradient-time relationship, pulse frequency, fluid properties, and tube radius, and they give the fluid velocity as a function of the above quantities and the radial position in the tube. A pulsatile flow apparatus was constructed which would allow measurement of all the variables mentioned above, and a computer program based on Womersley's equations was used to calculate the fluid flow rate and velocity profile from the pressure gradient-time relationship, fluid properties, and tube radius. Thus a comparison between measured and calculated values of flow and velocity could be made. Calculations and data agree within the estimated experimental error, thus providing evidence of the applicability of the theoretical equations to actual flow with large pulse amplitudes. The analog computer “pressure gradient technique” of D. Fry and associates was compared with the exact solution for straight rigid tubes and found to deviate less than 20% in amplitude and phase except at very low frequencies. hydrodynamics, pulsatile flow; blood flow, arterial; hemodynamics, pulse characteristics Submitted on April 6, 1964