On Stokes Flows in Channels and Pipes with Parallel Stationary Random Surface Roughness

TLDR: In this article, the Stokes flow problems of an incompressible viscous fluid in corrugated channels and pipes are considered and a pertubation solution is developed leading to an expression for the flow rate enhancement as a function of the statistics of the corrugations.

Abstract: The Stokes flow problems of an incompressible viscous fluid in corrugated channels and pipes are considered. The flow is parallel to the corrugations which are of small amplitude ϵ and are represented by stationary random functions. A pertubation solution is developed leading to an expression for the flow rate enhancement as a function of the statistics of the corrugations. Simplification of this expression are discussed. Das Stokessche Stromungsproblem eines inkompressiblen, viskosen Mediums in geriffelten Kanalen und Rohren wird betrachtet. Die Stromung verlauft parallel zur Riffelung, die von der kleinen Amplitude ϵ ist und durch stationare Zufallsfunktionen dargestellt wird. Eine Storungslosung wird entwickelt, die zu einem Ausdruck Fur das Anwachsen der Stromungsgeschwindigkeit als Funktion der Statistik der Riffelung fuhrt. Vereinfachungen dieses Ausdrucks werden diskutiert.