Influence of bed roughness and cross section geometry on medium and maximum velocity ratio in open-channel flow

This paper deals with the analytic-theoretical derivation of the relationships between the entropic quantity ?(M), representing the ratio between the mean and maximum flow velocities, and the relative submergence and aspect ratios, using classical open-channel flow equations. ?(M) is found to be highly dependent on the relative submergence when large or intermediate roughness scales occur, whereas it might be assumed to be almost constant for a small roughness scale. Furthermore, considering the hydraulic geometry relationships, an attempt is made to relate the relative submergence to the aspect ratio of flow through a log relationship whose coefficients depend on the local bed slope, with an important implication for hydrological practices. Then a practical relation between ?(M) and the aspect ratio is proposed and validated in an operative chain for discharge assessment that shows high robustness and stability. The proposed model has been applied to a set of experimental velocity data collected at gauged river sites with different geometric and hydraulic characteristics as well as low, medium, and high flows.