The Steady Slow Motion of a Non-Newtonian Liquid through a Tapered Tube

Abstract

A theory of the steady slow motion of a time-independent non-Newtonian liquid through a tapered tube is presented. The coefficient of viscosity µ which appears in the relationship between the stress and the rate of strain of a Newtonian liquid is assumed to be a function of the velocity gradient. Thus µ is a function of the coordinates of the liquid particles. The equations of motion of a non-Newtonian liquid through a tapered tube have been obtained under the following assumptions: i) the liquid is incompressible; ii) the motion of the liquid is laminar; iii) the motion is steady; iv) no body-force acts on the liquid; v) the motion has an axial symmetry; vi) there is no slip at the wall; vii) the stream-lines are straight lines passing through the vertex of the cone; viii) the motion is so slow that the inertia term can be neglected. The differential equation for the velocity distribution of a non-Newtonian liquid obeying power law has been derived.