Generalized Analytical Solutions for Alternate and Sequent Depths in Rectangular Open Channels: Sine Form

Abstract

Two novel generalized analytical solutions of nondimensional specific energy and specific force equations for flow in rectangular open channels are obtained, which enable direct and explicit calculation of the alternate and sequent depths for the given nondimensional specific energy and specific force, respectively. Hydrostatic pressure and uniform velocity distributions across flow depth have been assumed, and friction loss in the flow has been neglected, while deriving the new solutions. Each generalized solution yields only three particular solutions out of which only two solutions giving positive values for the depth of flow are of practical significance. The particular solutions/equations of practical significance pertain to the alternate depths and sequent depths in the cases of nondimensional specific energy and specific force, respectively, and are distinguishable for subcritical and supercritical flow. The new solutions are compact (handy), computationally simple, and useful to the field of engineers and practitioners in directly solving the problems of transitions in width and elevation of the channel bottom, hydraulic jump, and length of the stilling basins. Hopefully, these solutions will possibly end the persistent search for a long time for handy generalized analytical solutions of the specific energy and specific force equations in a rectangular open channel.