Direct Integration of the Equation of Gradually Varied Flow

The steady flow in open channels, when the depth of the flow varies gradually with distance, is governed by the classic gradually-varied-flow equation. The solution of this ordinary differential equation allows the tracing of the longitudinal profiles of the water surface of the flow. In this note, a relation, obtained by direct integration, is proposed for a wide rectangular channel, when Manning's formula is used, for the computation of the energy slope. Then, the profiles for subcritical and supercritical flow in a mild and steep channel are presented and a comparison with the Bresse solution, relative to the same channels, is carried out