On the flow of rotating fluid past bodies in a pipe

Abstract

This paper deals with the flow of a rotating, incompressible fluid through contractions and expansions of a pipe, or past bodies of revolution on the pipe axis. The flow far upstream is assumed to have constant axial velocity, and constant angular velocity about the pipe axis. The flow fields are constructed from the stream functions of a ring source on the pipe wall or of a point source on the pipe axis. These solutions involve wave motions when the angular velocity exceeds a critical value. The point-source solution is expressed in two forms, the first of which is useful some distance from the source, while the second displays more clearly the nature of the singularity and leads to a comparison of the corresponding doublet with Taylor's doublet solution (1922). Some streamline pictures and velocity distributions are presented, and the physical behaviour of a rotating fluid is discussed.