Secondary Flows in Pipes

Abstract

In Lecture 10 we have seen that steady rectilinear flow down a straight pipe is possible for a general incompressible fluid only for certain exceptional cross-sections, and for all cross-sections only for certain exceptional fluids. Both the Navier-Stokes fluid and the fluid of second grade are exceptional in this sense, since their viscometric functions satisfy the special relation (10.21). If a general fluid is forced by a pressure gradient down a pipe bounded by a cylindrical surface that is neither a pair of parallel planes nor a pair of coaxial circular cylinders, we expect that a steady flow be set up, but it cannot be rectilinear. The component of velocity normal to the generation of the cylindrical boundary is called a secondary flow.