Equivalent roughness height for plane bed under steady flow

This paper presents a new relationship between the roughness height and the main hydrodynamic and sediment parameters for plane beds under steady current conditions. In order to derive such a formula, a large data base involving plane-bed experiments was compiled from previous investigations and analyzed. Comparisons between the data and different existing predictive formulas for the bed roughness obtained from the literature were also made. A relationship with the Shields parameter only, which is commonly proposed, appeared to be insufficient. The roughness was also found to be a function of a Froude number and a dimensionless settling velocity. A critical Shields parameter was identified up to which the equivalent roughness ratio is proportional to the Shields parameter. The new empirical equation that was developed yields the best results for all conditions investigated, and should improve the understanding of the total shear stress.