Incompressible Potential Flow Past Axisymmetric Bodies in Cylindrical Pipes

Abstract

SummaryVandrey’s procedure, based on the method of singularities (ring vortices), for finding the pressure distribution on an axisymmetric body in a uniform stream is extended to the case of flow past a similar body in a uniform stream within a cylindrical duct of infinite length. The final form of the integral equation for the velocity distribution on the body is the same as that given by Vandrey; however, its kernel possesses additional terms representing the influence of the duct. Numerical solutions are worked out for varying radii ratio between a sphere and a duct and also between the more general-shaped axisymmetric body and a duct.