Free overall in circular channels with flat base: a method of open channel flow measurement

Abstract

A free overfall at the end of an open channel offers a simple means of measuring flow discharge. In this paper, two methods are presented for the computation of end-depth and discharge of a free overfall from smooth circular channels with flat base. Firstly, 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 experimentally determined pressure coefficient. In subcritical flows, the EDR is related to the critical-depth that occurs far upstream. In supercritical flows, the Manning equation is used to express the end-depth as a function of streamwise slope of the channel. Methods to estimate discharge from the end-depth in subcritical and supercritical flows are presented. The upstream flow profiles of a free overfall are computed using the streamline curvature at free surface. Secondly, an alternate method for analyzing free overfall from circular channels with flat base is also presented, where a free overfall in a circular channel with flat base is simulated by the flow over a sharp-crested weir to calculate the EDR. The comparisons of the computed results with the experimental data are satisfactory for subcritical flow and acceptable for supercritical flow.