Choke-free flow in circular and ovoidal channels

Abstract

A comprehensive solution for circular and ovoidal channel sections is obtained under the condition of choke-free flow owing to a gradual and smooth rise in bed elevation. Generally, two practical cases of channel transition are considered: (a) rising bed elevation caused by a change in the position of the channel centreline; and (b) rising bed elevation caused by a decrease in the channel diameter. Considering the critical flow occurring downstream of the transition zone, the energy equation is solved with the aid of a numerical technique to determine the explicit equations for the maximum allowable bed rise under a given approaching regime. Moreover, to determine the limits of upstream flow depths (the choke-free regions) from the information on upstream channel geometry, rise in bed elevation and discharge, suitable graphical solutions are presented using dimensionless specific energy equations. These graphs can be utilised to choose the operating ranges of upstream flow depths for choke-free flow in both subcritical and supercritical upstream flow conditions. Since the downstream critical depth is required to determine the upstream operating range, the direct solutions for critical depths in circular and ovoidal channels are also presented. Finally, energy loss in the transition zone is considered by applying it in the proposed equations.