Multiple Critical Depth Occurrence in Two-Stage Cross Sections: Effect of Side Slope Change

The critical flow concept has many applications in open-channel flow problems. Determination of critical depths for canals and natural streams with different shapes is a classic task, but important for efficient hydraulic design. Generally, critical depth is used to classify the flow into subcritical and supercritical and may be used as a control point for computing water surface profiles in steady and unsteady gradually varied flows. For a given compound channel, the kinetic energy correction coefficient varies quite rapidly above the overbank level. In such a case, specific energy may have more than local minimum or maximum (multiple critical depth) for some combination of discharge and geometry. The compound channels are well documented in the literature, but occurrence condition of the multiple critical depth has not yet been determined. The first step in modeling critical depth is to determine whether multiple occurrences exist. In current research, symmetrical prismatic channels with two different side slopes (two-stage cross sections) are considered, and the condition for which multiple critical depths exist is mathematically determined. For this, an analytical procedure is used to determine limiting side slope for the upper portion of the cross section. If the side slope of the upper portion is milder than the limiting side slope, the multiple critical depths will occur in the two-stage cross section.