Normal‐Depth Calculations in Complex Channel Sections

Abstract

The general problem of solving for normal flow depth in open‐channel flow has a complication in that some types of channel cross sections do not always have a unique solution. This paper analyzes an alternative iterative procedure for quickly and accurately solving the implicit problem of determining the normal flow depth in complex channel sections. Conditions that guarantee a unique solution and guarantee that the iterative procedure will converge to the solution are developed. A computer program for quickly and accurately finding the unique solution, using the Chezy or Manning flow resistance equations, is available. Test runs for a rectangular, a triangular, a trapezoidal, and two complex channel cross sections are used to evaluate the effectiveness of the procedure. The test results show that the iterative procedure presented here meets the requirements of guaranteed convergence, computational efficiency (speed and accuracy), and the ability to handle both trapezoidal and complex channel cross sections.