Uncoupled Laminar Duct Flows

Abstract

In duct flows, e.g., Fig. 1.2(a), the velocity field is said to be fully developed when u / u ₀ is a function of y only, independent of x. In this case, it follows from the continuity equation that the normal velocity component υ is zero everywhere, and the solution of the momentum equation for two-dimensional or axisymmetric uncoupled laminar flows can be obtained exactly and very easily. Clearly this is a particularly simple case of profile similarity, in which the y scaling factor is independent of x. Equally clearly, it applies only to flows in ducts of constant cross section, specifically circular ducts (pipes) and rectangular ducts whose cross section is so wide compared with its height that the flow at some distance from the side walls is near enough two-dimensional.