A method for determining the frictional velocity in a turbulent channel flow with roughness on the bottom wall

A method is proposed for determining the frictional velocity U-tau on both walls of a fully developed turbulent channel flow, one smooth and the other rough. This should aid experimentalists in obtaining a reliable estimate of U-tau with knowledge of only the pressure drop and location where the Reynolds shear stress is zero. The method is general and does not depend on the roughness geometry that is used. It has been validated against direct estimates of the wall stress using DNS databases for two types of two-dimensional roughness. Results for a surface composed of staggered cubes are also in accord with the method.