Flow in Straight Ducts of Arbitrary Cross Section

Abstract

A method is presented for treating flows in straight ducts. The method involves the conformal mapping of the cross section on to a semicircle, and then solving the problem using Fourier series. For oscillatory flows (to which most of the paper is devoted) the method results in an infinite, coupled system of differential equations, although reliable numerical results may be obtained by truncation. For steady flows, however, the method yields a solution involving integrals of the Jacobian of the transformation.