Free overfall in inverted semicircular channels

This paper presents a theoretical and experimental study on free overfall in a smooth inverted semicircular channel. Applying the momentum equation based on the Boussinesq approximation, the flow upstream of a free overfall is theoretically analyzed to calculate the end-depth-ratio (EDR). This approach eliminates the need of an empirical pressure coefficient. In subcritical flows, the EDR related to the critical depth is found to be 0.705 for critical depth-diameter ratio up to 0.42. In supercritical flows, the Manning equation is used to express the end-depth as a function of the streamwise slope of the channel. Methods to estimate discharge from the end-depth in subcritical and supercritical flows are presented. The discharge is also related to the end-depth and a characteristic parameter of the channel. The upstream free surface profiles are computed using the streamline curvature at free surface. The computed and experimental results are in satisfactory agreement in subcritical flow and have a slight discrepancy in supercritical flow.