Axisymmetric Stokes flow through a circular orifice in a tube

Abstract

Axisymmetric Stokes flow through a circular tube with a thin orifice inside is investigated. At far upstream and downstream from the orifice, the Hagen–Poiseuille flow exists in the tube. The problem is investigated by considering Stokes equation analytically using a complex eigenfunction. Flow properties such as stream function and pressure distribution are determined. From the results, the streamline pattern and pressure distribution are drawn. The excess pressure drop due to the orifice and the force exerted on the orifice are calculated as functions of the radius of the orifice.