Difference-Differential Equations for Fluid Flow in Distensible Tubes

The solution by Womersley of the Navier-Stokes equations for fluid flow in distensible tubes has been most useful to students of hemodynamics. However, this solution requires linearization, and, because results are obtained after transformation into the frequency domain, nonlinear or time-varying effects are not easily added. Analog, hybrid, or digital computer simulation require that difference-differential equations be obtained. This proves to be readily possible by returning to the Navier-Stokes and continuity equations, and using ordinary difference techniques in the space dimensions.