On blockage coefficients: flow past a body in a pipe

Abstract

Blockage coefficients characterize the presence of an object on uniform flow along a rigid pipe. The main purpose of the paper is to develop analytical methods for the calculation of these coefficients. For potential flow, blockage coefficients are related to the added mass of an object moving along a pipe. They also arise when matched asymptotic expansions are used to solve acoustic problems, in which Laplace’s equation is appropriate for related inner problems. Steady diffusion problems can also lead to similar harmonic problems. The paper includes some general results (such as a version of Webster’s horn equation for slender rigid objects) and some specific results for objects of various simple axisymmetric shapes (spheroids, spindles, finite circular cylinders, double cones and thin discs). Applications to various physical situations are expected in future work.