Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow

Abstract

The Reynolds number dependence of Cf, Uo, H and other bulk flow parameters in “two dimensional” (high aspect ratio) rectangular duct flow is explored and the empirical relations Cf = 0.073 Re−1/4 and Uo/U¯ = 1.28 Re−0.0116 are presented. The values A = 2.12 and K = 0.41 for the log-law constants and Π = 0.14 for Coles’ wake parameter are derived and are shown to be independent of Re. The integration of Dean’s formula for the complete velocity profile provides close agreement with all parameters when these values of A, K and Π are used and is shown to coincide with the “optimum log-law” for skin friction (which contains Π).