# Pulsatile Flow in an Elastic Tube

• M. Zamir
Chapter
Part of the Biological Physics Series book series (BIOMEDICAL)

## Abstract

In the case of a rigid tube it is possible to postulate a fully developed region away from the tube entrance where the flow is independent of x , thus derivatives of U , v with respect to x are zero. The equation of continuity combined with the boundary condition v = 0 at the tube wall then leads to v being identically zero and the governing equations reduce to
$$\rho \frac{{\partial u}}{{\partial t}} + \frac{{\partial p}}{{\partial x}} = \mu \left( {\frac{{{\partial ^2}u}}{{\partial {r^2}}} + \frac{1}{r}\frac{{\partial u}}{{\partial r}}} \right)$$
(Eq.3.2 .9) As we saw in Chapter 4, the pressure gradient term in that case is a function of t only, not of x, and the velocity U is then a function of r, t only, not of x. For an oscillatory pressure gradient the velocity U then oscillat es with the same frequency, and since it is not a function of x, it will represent the velocity at every cross section of the tube. The fluid then oscillates in bulk, or “en mass. ” There is no wave motion when the tube is rigid .

### Keywords

Attenuation Sine

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