Complete Velocity Profile and “Optimum” Skin Friction Formulas for the Plane Wall-Jet

Abstract

An analytic expression for the complete velocity profile of a plane, turbulent wall-jet in “stagnant” surroundings is obtained by coupling Spalding’s single formula for the inner layer with a sine function for the “wake component.” This expression is transformed at the velocity maxima to yield an “optimum log-law” for skin friction. An approximate skin friction formula based on the “initial conditions” of the wall-jet is also presented. The formulas are generally in good agreement with experimental data. The complete velocity profile does not exhibit the conventional “law of the wall” behavior and modifications are consequently recommended to the usual treatment of the near-wall region in numerical calculation procedures for wall-jet flows. The use of the “Clauser plot” method of skin friction measurement is similarly shown to be in error when applied to wall-jets.