Quasi-theoretical end-depth–discharge relationship for trapezoidal channels

SummaryFree overfall at the abrupt end of a channel offers a simple method for measurement of discharge from a single measurement of depth of flow at the brink. The theoretical procedure applied to compute discharge over a weir is applied to the free overfall to obtain end-depth–discharge relationship for subcritical and super critical flows. Pressure distribution at the brink, which is assumed a quadratic parabola, is incorporated in the analysis. A closed form equation for discharge in terms of end depth for subcritical flows was proposed and validated earlier with available experimental data in place of a derived implicit complex equation. Direct solution for discharge for known end depth is provided in the graphical form for super critical flows. Verification of this solution with available experimental data revealed that comparison is not as good as it is observed in subcritical flows. The difference in computed and observed results is attributed to the greater effect of streamline curvature and estimation of pressure factor in the supercritical flows.

► Free overfall at the abrupt end of a channel offers a simple method for measurement of discharge.
► Experimentally obtained pressure factor is used in the analysis.
► The difference in computed and observed results is attributed to the greater effect of streamline.