Laminar Fluid Transients in Conduits of Arbitrary Cross Section

Abstract

Conduit cross sections of nonelementary shape are the rule in biological fluid systems. Because of mathematical and experimental difficulties, however, relatively little is known about the dynamics of flow in these vessels, particularly under time-varying conditions, although knowledge of the fluid motion therein in terms of properties such as driving head, velocity, and wall shear stress is clearly essential for proper diagnosis of a flow problem. This paper presents an analytical method for solving problems of unsteady laminar flow in long ducts of arbitrary cross section. The implied assumption of parallel flow renders the mathematical situation linear, but the proposed method is far from conventional because it allows consideration of almost any cross-sectional configuration conceivable. This novel approach is made possible by joining a steady-state superposition method for creating new conduits from known basic shapes with a regular perturbation scheme found suitable for dealing with fluid transients in circular pipes. The method is developed step by step, and the results are applied to an example with biomedical implications.