Helical Flow of General Fluids

Abstract

The problem of the helical flow of a general fluid is solved making no special constitutive assumptions other than incompressibility. It is shown that from a knowledge of the rheologists' viscosity function one can calculate the dependence of the velocity field in helical flow on the geometry and applied forces. The complete stress distribution (including normal stresses) may be calculated from a knowledge of three basic material functions which can, in principle, be determined from an experimental study of simple shearing flow. Expressions are derived for the discharge rate and for the angular velocities of the bounding cylinders as functions of the applied forces.