Computation of gradually varied flow in compound open channel networks

Abstract

Although, natural channels are rarely rectangular or trapezoidal in cross section, these cross sections are assumed for the computation of steady, gradually varied flow in open channel networks. The accuracy of the computed results, therefore, becomes questionable due to differences in the hydraulic and geometric characteristics of the main channel and floodplains. To overcome these limitations, an algorithm is presented in this paper to compute steady, gradually varied flow in an open-channel network with compound cross sections. As compared to the presently available methods, the methodology is more general and suitable for application to compound and trapezoidal channel cross sections in series channels, tree-type or looped networks. In this method, the energy and continuity equations are solved for steady, gradually varied flow by the Newton–Raphson method and the proposed methodology is applied to tree-type and looped-channel networks. An algorithm is presented to determine multiple critical depths in a compound channel. Modifications in channel geometry are presented to avoid the occurrence of multiple critical depths. The occurrence of only one critical depth in a compound cross section with modified geometry is demonstrated for a tree-type channel network.