Effect of bed roughness on 1-D entropy velocity distribution in open channel flow

A theoretic-analytical formulation, based on entropy velocity profile law and classical relationships for uniform flow and friction factor, is proposed enlightening the general logarithmic relationship existing between the parameter Phi(M), defined as mean cross section velocity over maximum velocity, and the ratio water depth/bed roughness (D/d). The relationship Phi(M) D/d has been applied to a relevant set of experimental velocity measurement data collected both in laboratory and in field, showing different behaviour between small scale and large-intermediate roughness flows. In particular, the roughness influence becomes remarkable whenever shallow water flow conditions occur, that is when the ratio between the flow depth and the roughness height is less than 4, while Phi(M) tends to be constant as the value of Dd increases.