Flow through a converging-diverging tube and its implications in occlusive vascular disease — I: Theoretical development

Abstract

The steady flow of an incompressible fluid through an axisymmetric converging-diverging tube has been studied both theoretically (Part I) and experimentally (Part II). Possible implications of this type of flow in the development of vascular lesions are discussed in Part II. A mathematical model for a mild stenosis is established and an approximate solution for flow through a converging-diverging tube obtained. Velocity profiles, pressures, and wall shearing stresses along the tube are determined from this solution. The critical Reynolds number required for separation, and the extent of the separated region are also determined.