Flow in the Entrance Region of a Porous Pipe : 4th Report: Oscillatory Flow

Abstract

This study deals with an axisymmetric oscillatory flow of an incompressible viscous liquid in a circular porous pipe, which starts from rest. Change of the axial velocity profile over an arbitrary cross-section of the pipe duet to a step change and/or an oscillatory one of the flow rate is analytically obtained including a transient component of the velocity in the inlet region. The present analysis is based on Oseen's approximation of the momentum equation and the validity of this method is confirmed by the modified momentum integral method. Dynamic distributions of wall friction and pressure coefficients are precisely discussed on the boundary conditions for oscillatory injection and suction from the pipe wall. Furthermore the following two facts are made clear : one is that slip velocity on the wall has an immediate connection with wall friction, the other is that both the alternating component of the axial velocity and the slip velocity on the wall make the inlet short.