Pulsatile Flow in a Rigid Tube

Abstract

Flow in a tube in which the driving pressure varies in time is governed by Eq.3.2.9, namely,

$$\rho \frac{{\partial u}}{{\partial t}} + \frac{1}{\rho }\frac{{\partial p}}{{\partial x}} = \mu \left( {\frac{{{\partial ^2}u}}{{\partial {r^2}}} + \frac{1}{r}\frac{{\partial u}}{{\partial r}}} \right)$$

Providing that all the simplifying assumptions on which the equation is based are still valid, the equation provides a forum for a solution in which the pressure p is a function of x and t while the velocity u is a function of r and t. Before obtaining this solution, it is important to reiterate the assumptions on which the equation is based, because these assumptions define the idealized features of the flow that the solution represents.