Hydrodynamical Entrance Length Effects for Duct Flows With Arbitrary Inlet Velocity Profiles

Abstract

An existing analytical method for predicting the entrance region pressure drop and relating effects in straight ducts of arbitrary cross section is generalized to include the application of arbitrary inlet velocity profiles. The only requirement for the use of the derived theoretical results is the availability of integrable (analytically or numerically) expressions for the inlet and the fully developed velocity profiles for the cross-sectional geometry under consideration. The derived results are applied to the case of the transition of fully developed laminar tube flow to fully developed circular-sectorial flow. The latter may be induced by the introduction of a flow divider into the tube. The numerical results are tabulated and also presented graphically.