Computation of Flow Transitions in Open Channels with Steady Uniform Lateral Inflow

Abstract

A numerical procedure is developed for quickly and accurately finding the location and flow depth of a flow transition (critical control section) in open channels with discharge gradually varying along the channel length. General equations are presented for trapezoidal, triangular, and rectangular cross sections. A numerical analysis of the procedure shows that the geometry of the channel cross section is an important factor determining the existence of a unique solution to the flow‐transition problem in open channel flow. A procedure is described to decide if solutions exist and, if they do, to compute them and select an acceptable solution as the starting point for water‐surface profile calculations. Test runs on a computer are performed to verify the speed and accuracy of the proposed procedure. Examples involving the finding of location of flow transitions in open channels are used to illustrate the usefulness of the procedure. The findings from this study are beneficial to hydraulic engineers solving problems related to the design of lateral spillway channels and gutters for conveying stormwater runoff; to hydrologists using spatially varied flow equations to describe flow processes in natural channels; and to the enhancement of algorithms for spatially varied flow computations in hydrologic simulation models such as the CREAMS field‐scale model and the WEPP watershed model.