Visualization of Specific Energy for Open Channel Flow in Three Dimensions

Abstract

Specific energy is the total head with respect to the channel bottom. It is a summation of the velocity head and the depth of flow at a given cross section. Specific energy has proven to be very useful in the analysis of open channel flow and the concept is discussed in every open channel book. Usually, the discussion is illustrated by 2-dimensional plots of depth vs. specific energy with discharge as a parameter and/or depth vs. flowrate with specific energy as a parameter. Obviously, these graphs depict slices through a surface in a three-dimensional space whose coordinates are depth, discharge, and specific energy. Furthermore, the plots are almost invariably displayed only for rectangular cross sections, and the three-dimensional specific energy surface is rarely shown. Using graphical software, this paper displayed the specific energy function as a surface in three dimensions for rectangular cross sections. For the first time, the specific energy function is also visualized in three dimensions for rectangular and trapezoidal cross sections as well as a compound channel cross sections, revealing unexpected features. Above all, this study is particularly meaningful in expressing alternate depth and critical water depth in an effective way that only a few researchers have tried to express before.