Testing flow resistance equation for rill flow

Abstract

At first, in this paper a flow resistance equation for rill flow, deduced applying dimensional analysis and self-similarity theory, is presented. The incomplete self-similarity hypothesis is used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy-Weisbach friction factor. Then the deduced theoretical resistance equation, which is calibrated by some measurements of flow velocity, water depth, cross section area, wetted perimeter and bed slope carried out in 106 reaches of some rills modelled on an experimental plot, is tested using the literature data by Abrahams et al. (1996), Strohmeier et al. (2014) and Peng et al. (2015) for rill flows. The relationship among the velocity profile, the channel slope and the flow Froude number is also calibrated using all available data. Finally the analysis shows that the Darcy-Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power-velocity profile.