A Relatively Simple Integral Method for Turbulent Flow Over Rough Surfaces

The integral form of the equation for x momentum is solved for the skin friction coefficient, in external thin boundary layer flow, on surfaces whose technical roughness elements' size is given. This is done by using a “roughness depression function” in the law of the wall and wake which serves as the needed velocity profile. The method uses the equivalent sand grain size concept in its calculations. Predictions are made of the friction coefficient, Cf, as a function of momentum thickness Reynolds number and also, of Cf's dependence on the ratio of momentum thickness to the size of the technical (actual) roughness elements. In addition, boundary layer thicknesses and velocity profiles on rough surfaces are calculated and, when available, comparisons are made with the experimental data from a number of sources in the literature. Also, comparisons are made with the results of another major predictive scheme which does not use the equivalent sand grain concept.