New Flow-Resistance Law for Steep Mountain Streams Based on Velocity Profile

Abstract

This paper deduces a new flow-resistance equation for open-channel flow applying dimensional analysis and self-similarity theory. The incomplete self-similarity hypothesis is used to establish the flow velocity distribution whose integration gives the theoretical expression of the Darcy-Weisbach friction factor. The theoretical resistance equation then is tested by the available field measurements of flow velocity, water depth, river width and bed slope carried out in 653 reaches of several Canadian mountain streams. A relationship between the Γ function of the velocity profile and the channel slope and the flow Froude number is also established. The analysis shows that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power-velocity profile. Finally, the Darcy–Weisbach friction factor values obtained by the proposed theoretical resistance law are compared with those estimated by the approach of Rickenmann and Recking.