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.

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In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, is tested experimentally on plots of varying slopes in which mobile bed rills are incised. Initially, measurements of flow velocity, water depth, cross‐sectional area, wetted perimeter and bed slope conducted in 106 reaches of rills incised on an experimental plot having a slope of 14% were used to calibrate the flow resistance equation. Then, the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number, which was calibrated using the 106 rill reach data, was tested using measurements carried out in plots having slopes of 22% and 9%. The measurements carried out in the latter slope conditions confirmed that (a) the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the data were supportive of the slope independence hypothesis of rill velocity stated by Govers.

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