A boundary condition for turbulent flow along a rough surface

A boundary condition for turbulent flow along a rough surface is formulated using simple qualitative arguments. The condition defines the fictitious sliding velocity on a conditional smooth surface passing through the tips of roughness protrusions. By using Nikuradze's (1933) experiments and experimental data on resistance in smooth tubes, the mixing paths on the wall and the sliding coefficient are determined as a function of the roughness. An approach similar to that of Van Driest's (1956) is used together with the boundary condition to determine the dependence of the damping coefficient at the solid wall on the roughness.