Flow resistance equation for rills

In this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self-similarity theory. At first, the incomplete self-similarity hypothesis was 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 was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy-Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power-velocity profile.