End Depth in Circular Channels

Abstract

The flow upstream of a free overfall from smooth circular channels is theoretically analyzed to calculate the end-depth ratio (EDR), applying the momentum equation based on the Boussinesq approximation. The present approach eliminates the need for an empirical pressure coefficient. In subcritical approaching flows, the EDR is related to the critical depth, which occurs upstream of the end section, and the value of EDR is found to be around 0.75 for a critical depth-diameter ratio up to 0.82. On the other hand, in supercritical approaching flows, the end depth is expressed as a function of the streamwise slope of the channel using the Manning formula. Simple methods are presented to estimate the discharge from the end depth in subcritical and supercritical approaching flows. A relationship of discharge to the end depth and the channel characteristics parameter is also proposed. Streamline curvature at the free surface is used to compute the flow profiles upstream of a free overfall. This paper also presents a theoretical model to analyze the free overfall from horizontally laid rough circular channels with the aid of an autorecursive search scheme.