Deducing the stage-discharge relationship of rectangular broad and sharp-crested contraction devices

Flumes with a local contraction of the channel width are a common way for accurately measuring the flow discharge. In this paper, the outflow process of rectangular broad and sharp-crested contraction devices is modeled using the dimensional analysis and the incomplete self-similarity condition. The proposed theoretical stage-discharge relationship is tested using measurements available in the literature. The proposed power equation is characterized by a value of the exponent close to 1.5 and a coefficient depending on the contraction ratio. The proposed flow-measuring flumes are characterized by a good accuracy of the measured discharge (ranging from -2.71 to 3.28% for the broad-crested contraction device and in the range from -0.24 to 0.31% for the sharp-crested one). Even if both flume types have good accuracy of the measured discharge (less than the limit of ±5% suggested in the literature), the developed analysis demonstrated that the sharp-crested device is characterized by the lowest values of the errors in the estimate of discharge, and this result increases the interest of this device in practical applications. The advantage of the proposed approach is combining an accurate estimate of the flow discharge and working regardless of the discharge coefficient estimate.