The flow upstream of a free overfall from smooth inverted semicircular channels is theoretically analysed to compute the end-depth ratio (EDR), applying an energy equation based on the Boussinesq assumption. This approach eliminates the need for an experimentally determined pressure coefficient. Experiments were conducted with horizontal channel conditions. The EDR related to the critical depth, which occurs upstream from the end section, is found to be around 0.695 for a critical depth-diameter ratio up to 0.40. A simple method is presented to estimate the discharge from a known end-depth. The theoretical model corresponds closely with the experimental data.