Analytical Solution of Gradually Varied Flow Equation in Non-prismatic Channels

Computation of water surface profile in open channel is considered as an essential component of channel design in open-channel hydraulics. In this regard, gradually varied flow (GVF) is enumerated as the most frequently occurring flow regime in artificial open channels. The analytical and/or semi-analytical solutions of GVF have been acquired for some types of open channels with prismatic channel cross section using both Manning’s and Chezy’s resistance equations. In conventional hydraulic textbooks, the interpretation of water surface profile is mainly based on prismatic channels. Indeed, the non-prismatic term in the numerator of the governing equation creates a further obstacle for proper interpretation. In this paper, an explicit closed-form semi-analytical solution is presented for a non-prismatic rectangular channel based on Chezy’s resistance equation using Adomian decomposition method. The developed semi-analytical solution compares well with both analytical and numerical solutions obtained from predictor–corrector method with very fine spatial resolution. The derived semi-analytical solution can be effectively used to conduct sensitivity analysis of pertinent parameters and compute channel discharge for a given water surface profile.