Multi-Critical Water Depths and Precise Discharge Determination for Symmetrically Compound Channel in Unsteady State Flows

The critical depth, which making unstable flow situation for necessary avoiding on design, of channel flow influences the water-surface profile obviously, and it defines the relationships between specific energy and discharge. Generally speaking, for a given discharge and the shape of cross-section, the minimum specific energy will have the corresponding only one critical depth as the initial condition for computing the steady gradually varied flow. In this paper, we will discuss the situation of critical depths on symmetrically compound channel flows in unsteady state incorporating a general definition of Froude number based on the 1D unsteady momentum and continuity equations with the self-derived 3D velocity profile. With the self-derived velocity profile, the critical depth may be calculated step-by- step and the precise discharge determined and compared. Examples for calculations and comparisons for critical depth and discharge are given and some discussion also presented finally.