Variability of the slope of the energy grade line with a change in water surface elevation

The computation of gradually-varied-flow profiles involves the solution of the equation of gradually varied flow. The objective of the computation is to determine the water-surface elevation along a channel or the flow profile. The Standard Step Method, which is applicable to nonprismatic channels, is one method of computation. One can either start the computations with a known water surface elevation or, if the water surface elevation is unknown, an estimated value for the slope of the energy grade line (EGL). A common practice by some persons and an option in some computer programs is to estimate the slope of the water surface and use this value as the slope of the EGL. Although this approach will give an answer, the variability of the slope of the EGL with a change in water surface elevation makes the results unreliable. Through comparison of the slope of the EGL versus water surface elevation for eight (8) sites on six (6) different rivers in Missouri, it is shown that the estimated slope of the water surface is not a good indicator of the slope of the EGL. The trend or the degree of the change in the slope of the EGL versus water surface elevation is not the same for all the rivers investigated, or the same for a single river at different locations. Through comparison of the slope of the EGL versus water surface elevation for a generic cross section, it is shown that between the aspect ratio of the cross section and the roughness coefficients, the roughness of the cross section has the greatest effect --Abstract, page iii