Flow-Through Short-Crested Trapezoidal Weirs: Effect of Downstream Slope

Trapezoidal profiled weirs and barrages are employed extensively in agrarian countries like India and Pakistan for diverting river water for canal-fed irrigation. The downstream slope of a weir is designed as $1\mathrm{V}:3\mathrm{H}$, although in some older structures, slopes as mild as $1\mathrm{V}:5\mathrm{H}$ are noticed. Downstream slopes of $1\mathrm{V}:5\mathrm{H}$ also exist for the barrages on the Nile in Egypt and in the standard Crump weir used in the UK and some European countries. This study explores the effect of the downstream slope of a short-crested trapezoidal weir on its flow hydraulics and conveyance properties. Irrigation barrages and weirs, apart from diverting water to a canal, also help in measuring the discharge of a river, which is a function of the up- and downstream water levels. For large discharges during floods, the gates of a barrage are withdrawn to ensure an uncontrolled flow that may either be free or submerged, depending on the downstream water level. Although past studies on uncontrolled flows have recognized the effect of the upstream slope of a weir on the coefficient of discharge, $C_d$, this study establishes that it is also influenced by a weir’s downstream slope. An equation of $C_d$ for free flows and a flow reduction factor for submerged flows are proposed considering both weir-face angles. For free flows, $C_d$ is seen to increase with the steepness of a weir’s downstream slope; for submerged flows, the discharge reduction factor is observed to improve as the slope becomes milder, leading to a greater conveyance. Data from our own laboratory experiments, past publications, and results derived from a 2D RANS-VOF multiphase computational fluid dynamics model are used in arriving at the conclusions reported in the study.