New Approach for the Calculation of Critical Depth in a U-Shaped Channel

The U-Shaped channel is a high performance structure widely used in practice. Currently, the problem of the critical depth in such profile does not have a direct solution. Current methods of calculation are based on complex mathematical procedures or optimal fitting methods, often generating unacceptable errors in practice, knowing that the calculation of the critical depth requires a high accuracy. The complexity of the problem stems from the fact that the flow governing equations are complicated due to the shape of the profile. In this study, the form of the flow equation is simple through the intake of the properties of the triangle. Furthermore, even if the equation is implicit, its resolution is possible by applying the fixed-point method with an initial value judiciously chosen. The process converges after the seventh step of calculating only and leads to an almost exact solution. A calculation example is presented that highlights the simplicity of the calculation procedure.