Theory of the Steady Slow Motion of Non-Newtonian Fluids through a Tapered Tube

A theory of the steady slow motion of non-Newtonian fluids through a tapered tube is presented. It is assumed that the fluid is characterized by a time-independent flow curve and that the tapering angle is very small. It is further assumed that the coefficient of viscosity η which appears in the relationship between the stress and the strain rate of a non-Newtonian fluid is not a constant, but a function of the velocity gradient. General formulae for the shear stress, velocity and flow are obtained. These formulae are similar to those for a straight tube of uniform cross section.