A direct theory of viscous fluid flow in pipes II. Flow of incompressible viscous fluid in curved pipes

Abstract

This paper is a companion to Part I under the same title and is concerned with the development of an analytical solution (via a direct formulation) for flow of an incompressible viscous fluid in curved pipes. Although a major portion of the analysis is presented for circular pipes of elliptical cross section, detailed calculations are carried out only for pipes of circular cross section. These calculations include the friction loss factor and the velocity contours, both of which are presented over a range of Dean number th a t significantly goes beyond the corresponding range of recent numerical solutions and the available experimental data. The results obtained show very favourable agreements with existing experimental data and several recent numerical solutions of the same problem based on the Navier—Stokes equations. Also included (for pipes of circular cross section) is a comparison of the multiple solutions and bifurcation points, as predicted by the present analytical solution, with corresponding available inform ation from several recent num erical solutions of the problem.