Skin Friction Correlation for Smooth and Rough Wall Turbulent Boundary Layers

In this paper, we propose a novel skin friction correlation for a zero pressure gradient turbulent boundary layer over surfaces with different roughness characteristics. The experimental data sets were obtained on a hydraulically smooth and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. The flow Reynolds number based on momentum thickness ranged from 3730 to 13,550. We propose a correlation that relates the skin friction, $Cf$⁠, to the ratio of the displacement and boundary layer thicknesses, $δ*∕δ$⁠, which is valid for both smooth and rough wall flows. The results indicate that the ratio $Cf1∕2∕(δ*∕δ)$ is approximately constant, irrespective of the Reynolds number and surface condition.