Leakage of a Fluid through a Narrow Channel with a Wavy Wall

Abstract

A theoretical study is made of two-dimensional flows of a viscous incompressible fluid in a narrow channel with a simple-harmonic wavy wall. The main object is to study the effect of the wave length and amplitude of the wavy wall on the leakage of the fluid through the channel. The decreasing rate of the discharge is proportional to the square of the ratio of the amplitude to the width of the channel. In case of a long wave, the problem can be solved analytically by the perturbation procedure; then the discharge decreases due to the wavy wall. In case of a medium wave length, the discharge decreases monotonically and makes the wave shorten. However, if the Reynolds number increases, the decreasing rate of the discharge first decreases and then increases, i.e., there is a minimum decreasing rate.