DISCHARGE VERSUS DEPTH CURVE FOR A GIVEN SPECIFIC ENERGY APPLICABLE TO ALL RECTANGULAR CHANNELS

Abstract

The aim of this paper is to present a universal discharge versus flow depth curve for any given Specific Energy, which is applicable to all rectangular channels. This is achieved by non-dimensionalizing the Specific Energy versus depth relationship for rectangular channels in such a way as to result in a single non-dimensional discharge versus non-dimensional depth curve. Unlike in the case of universal Specific Energy curve, this curve never approaches infinity and thus covers the entire theoretically possible range of flow depths and is still as useful as the unified Specific Energy curve, in determining flow depth for given discharge, Specific Energy and channel width, without iteration. It will also be shown that the universal discharge curve is easier to use in analyzing sudden width change problems and also gives a better intuitive feel for these problems whereas the universal Specific Energy curve is similarly better for sudden bed elevation change problems. For instance, the discharge curve confirms the well-known fact that when channel width suddenly contracts, flow depth decreases for supercritical flow and increases for supercritical flow. Such exercise with universal Specific Energy curves is inconclusive.