Incompressible flow in a duct with an arbitrary cross-section

Abstract

In this paper, the problem of finding the velocity profile of fully developed laminar flows through ducts of arbitrary cross-sections is investigated. The method which is used is based on a perturbative approach, although some nonperturbative exact results are also obtained. The main quantity which is addressed is the specific conductivity. This is a dimensionless quantity, which is independent of the size of the duct and the properties of the fluid, depending on only the shape of the duct. Some examples are studied is detail, for which the numerical values of the specific conductivity are determined, in the form of perturbative or exact results.