Resistance Coefficient of Uniform-Sand Roughness

The Weisbach resistance coefficient, f, is a boundary-drag coefficient. In the gross sense over a finite length of boundary, the coefficient is visualized as a skin-drag coefficient but over a rough boundary the coefficient is actually a spatially-averaged and time-averaged form-drag coefficient of the flow over the individual roughness elements. If uniform-sand roughness is considered, the form-drag coefficient should be a constant at high Reynolds numbers, since the geometry of the flow obstruction is independent of the sand size. The physically irrational variation of the resistance coefficient with relative roughness is simply the consequence of using the mean velocity of the gross stream rather than the actual flow velocity past the roughness elements in the evaluation of the drag coefficient.