Generalized Analytical Solutions for Alternate and Sequent Depths in Rectangular Channels: Nonuniform Velocity

Abstract

Novel generalized analytical solutions, in closed form, of hydraulic-energy and hydraulic-force equations governing the flow in rectangular open channels are derived considering the nonhydrostatic pressure and nonuniform velocity. The derived solutions are convenient, computationally simple, and enable direct and explicit calculation of the alternate and sequent depths in the case of nonhydrostatic pressure and nonuniform velocity over the flow depth. The generalized solutions yield only three particular solutions, of which two are of practical significance. The solutions of practical significance correspond to the alternate and sequent depths in the case of hydraulic-energy and hydraulic-force equations, respectively. The particular solutions/equations of practical significance are identifiable for subcritical and supercritical flow. The new analytical solutions would be of interest to academicians, field engineers, and practitioners in directly solving problems of transitions in channel sections and determining hydraulic jump elements and the length of stilling basins.