Development of an analytical benchmark solution to assess various gradually varied flow computations

Abstract

ABSTRACT Accurate quantification of water-surface profile and associated length plays a prominent role in open channel hydraulics. Traditionally, hydraulic engineers consider analytical solution for a wide rectangular channel (not available in reality) or solution from seemingly more accurate numerical schemes as yardstick to assess the efficiency of their proposed approach. In this paper, a closed-form solution of gradually varied flow equation is derived for ordinary rectangular and triangular channels using Manning’s formula as the resistance equation without any approximation in the conventional governing equation. It is believed that the proposed method of integration also works for channels with vertical sidewalls such as round-corner rectangular channels. This newly developed analytical solution paves the way for numerical analysts to assess gradually varied flow computations and provides practicing hydraulic engineers with the computational speed required for obtaining water-surface profile in open channels. Five different conventional schemes – in which the gradually varied flow equation is directly integrated after some simplifications and approximations – are compared and contrasted with the analytical solution obtained in this study. Furthermore, the accuracy of three numerical integration schemes as well as the HEC-RAS software is investigated, and it is observed that simple numerical methods in which the discretization is in depth rather than distance can give almost accurate results for the gradually varied flow equation. However, for the cases where discretization in distance is required, the numerical schemes including the standard step method in HEC-RAS have errors that can be assessed and quantified via the newly developed real analytical solution.