Hydraulics of free overfall in steeply sloping rough rectangular channel: A general computational approach

Abstract

All supercritical free overfalls were almost considered as frictionless flow or pseudo-uniform flow before, the effect of friction had not been paid due attention. Currently, a new mathematical model is proposed to analyze supercritical rectangular free overfall by Boussinesq-type energy equation accounting for frictional effect. A computational approach of loop iteration algorithm is utilized to simultaneously calculate the implicit water surface profile by Runge-Kutta method, end-depth-ratio, and discharge. Subsequently, the dependency of discharge on end depth and Nikuradse equivalent sand roughness for different slope is illustrated. Comparison of computed results with experimental observations reveals satisfactory agreement. Additionally, the present energy approach leads to more accurate results than the momentum method for high roughness. Finally, to aid application for engineers, an explicit solution of discharge for practical application in the commonly using range is also proposed. The most important purpose of this study is to present a general computational approach, which could be used for the rough supercritical free overfalls of any other cross-sections.