Direct integration of Manning-based gradually varied flow equation

Solution of the gradually varied flow equation allows tracing of the flow depth along a channel length. Direct solutions of this differential dynamic equation are available in the technical literature only for the special case of wide rectangular channels and for general rectangular channels based on the simple Chezy formula. No direct solution is available for the case of general rectangular channels based on the complex, but more realistic, Manning formula. This paper presents an approach for establishing the gradually varied flow profile for general rectangular channels through application of the Manning formula. The approach, which yields a very accurate computation of flow profiles, should be a useful tool for direct quantitative analysis and evaluations of general rectangular channels.