AN INNOVATIVE APPROACH TO CALCULATE THE CRITICAL DEPTH IN A TRIANGULAR SHAPED-CHANNEL

Abstract

This paper focuses on a procedure for the dimensioning of the triangular-shaped channel at critical flow, which is important in the practice of the hydraulic engineer. The proposed approach, which explores the potential offered by heuristic methods for solving complex optimization problems, is based on the use of an analytical method that is presented and applied for the calculation of the critical depth y<sub>c</sub>, which is governed by a cubic equation with no second-order term. The resolution of this equation is essentially based on Cardan's theorem. This method takes into account, in particular, the effect of the absolute roughness ε, the effect of the kinematic viscosity ν through the Reynolds number Re, and the effect of the channel bed slope S through the friction factor f. These parameters are easily measurable in practice. In this research, we relied mainly on the application of two universally accepted relations of Darcy-Weisbach and the Colebrook formula in a state of critical flow. Explicit relations are deduced that govern the critical depth, y<sub>c</sub>, by a particular examination of two cases; one is a turbulent flow over a smooth surface and the other is a flow over a rough surface.