Analytical integration of the equation of gradually varied flow for triangular channels

The solution of the gradually-varied-flow equation allows the tracing of the flow depth along a channel length. No closed-form solution is available in the technical literature for this differential equation for triangular channels based on Manning’s formula. In current research, by applying Manning’s formula, an analytical solution to compute the length of the gradually-varied-flow profile for triangular channels is derived. Moreover, the dimensionless profiles for subcritical and supercritical flow in both a mild slope and a steep slope triangular channel are presented. Finally, using the proposed solution, the computation steps of the discharge for a given triangular channel are presented. The direct solution presented in this study can be used for triangular irrigation ditches and triangular channels.