Direct Integration of Manning-Based GVF Equation in Trapezoidal Channels

Abstract

The direct integration method is used to compute free surface profiles in gradually varied flow (GVF) along the length of a prismatic open channel. Analytical solutions of the GVF equation, based on the Manning equation, are available in the technical literature only for the special case of triangular and wide rectangular channels. No closed-form (direct) solution is available for this equation for the case of trapezoidal channels. Open channels with trapezoidal cross sections are widely used as drainage, irrigation, urban stormwater, water transmission, and power channels. In the current study, by applying the Manning equation, a semianalytical solution to compute the length of the GVF profile for trapezoidal channels is derived. This solution, which allows an accurate computation of the flow profiles with minimal computational effort and time, should be a useful tool for direct quantitative analysis and evaluations of trapezoidal channels and thus should be of interest to practitioners in the water engineering community.