Stage-Discharge Rating Equation for an Elliptical Sharp-Crested Weir

Abstract

A new elliptical sharp-crested weir was developed to address discharge, pollution, and maintenance concerns associated with detention ponds. The elliptical weir was specifically designed to decrease the time and cost associated with clearing debris following storm events. A 2∶1 Froude-scale physical model was constructed and stage-discharge data were collected to analyze the stage-discharge relationship of the new weir. A total of 45 steady-state tests were conducted encompassing nine unique weir geometric configurations. The ellipse ratio varied from 12 to 16, and the gap width varied from 1.5 to 9.1 mm (0.005 to 0.030 ft). Empirical power-regression coefficients were determined for each of the configurations. Also, a theoretical rating equation was derived for the elliptical weir and a discharge coefficient of 0.642 was determined from analyzing the physical-model data. Trapezoidal integral approximation was used to develop an explicit approximate solution for the theoretical rating equation. By using the trapezoidal integral approximation, measured discharges were predicted with a mean absolute percent error of 3.55% for the data set, excluding discharges lower than 2.83 L/s (0.10 cfs).