Accuracy of energy and momentum principles for gradually varied analysis of flow through compound channels
18 September 2008
Compound section is a common shape for many natural rivers especially under flood flow resulting from natural or man-made phenomena such as heavy rainfall or dam failure. One-dimensional analysis of flow through compound channels in designing river and dam related hydraulic structures is widely used by engineers around the world. Accurate evaluation of tailwater stage-discharge rating curves for designing energy dissipaters and water surface profile calculations in channels downstream dams are examples where this kind of analysis may be required. Energy and momentum approaches can lead to different results in one-dimensional analysis of flow through compound channels and therefore a choice between these two equations must be made to analyse the flow. This investigation is an effort to provide some insight into the validity of these two approaches for one-dimensional analysis of steady gradually-varied flow through compound channels. To achieve this, first the energy and momentum equations and a comprehensive form of steady gradually-varied flow governing equation (GE) are introduced. As the GE shows, and it has been reported in the literature, the accuracy of the two approaches depend on two important factors: 1) correct evaluation of friction or energy slopes, and 2) selection of a proper functional form for Froude number. It is common practice to assume that energy and friction slopes are equal and can be estimated by typical resistance equations for corresponding steady uniform flow (conveyance estimation methods). This is a reasonable assumption and is justified because of the inexact empirical methods involved in evaluating the slopes. Then several computed water surface profiles corresponding to experimental data (M1, S1 and S2 types) are developed by combinations of different conveyance methods and Froude number definitions. Finally, experimental data collected in this study, and those reported in the literature, are used to compare different computed water surface profiles with laboratory measurements. The study indicates that the momentum principle is more consistent with corresponding steady uniform flow energy/friction slope for water surface profile computation in compound channels at least for the profile types considered in this study. Interestingly, this result is independent of the conveyance method used to estimate the corresponding steady uniform flow energy/friction slope.
