Analysis of Steady Laminar Flow of an Incompressible Newtonian Fluid Through Curved Pipes of Small Curvature

Abstract

Steady laminar flow of an incompressible Newtonian fluid through a curved pipe of small curvature is considered. The governing equations of flow are obtained in terms of secondary flow stream function and axial velocity component as suggested by Dean. A method of successive approximations is developed to solve these equations. The first five approximations are computed. The solution obtained is used to determine the axial velocity distribution, secondary flow pattern, axial pressure drop, and pressure distribution along the pipe wall. A semiempirical equation is obtained for axial pressure drop. The theoretical results obtained are compared with the available experimental data on axial pressure drop.