The Steady Flow of a Viscous Fluid through a Tapered Tube

Abstract

A theoretical investigation is made on the steady axisymmetric flow of an incompressible viscous fluid through a taperared tube. The velocity field is expanded into inverse powers of r, the distance from the virtual vertex of the conical tube, and the equations for the coefficient functions are solved successively. Distributions of the velocity, the pressure and the stress are determined to the second approximation, the first being the results obtained with the Stokes approximation. The flux of the flow per unit time is also calculated and shown to agree with that obtained with the Stokes approximation.