New Stage–Discharge Relationship for Triangular Broad-Crested Weirs

Abstract

Simple hydraulic structures, such as weirs, allow measuring flow discharge by using the upstream flow depth and a stage–discharge relationship. In this relationship, a discharge coefficient is introduced to correct all the effects neglected in the derivation (viscosity, surface tension, velocity head in the approach channel, flow turbulence, non-uniform velocity profile, and streamline curvature due to weir contraction). In this paper, the dimensional analysis and the incomplete self-similarity theory are used to investigate the outflow process of triangular broad-crested weirs, characterized by different values of the ratio between crest height p and channel width B, and to theoretically deduce a new stage–discharge relationship. A new theoretical stage–discharge relationship is suggested for the free-flow condition, and it is tested using experimental data available in the literature for the hydraulic condition p/B > 0. The obtained stage–discharge equation, characterized by low errors in discharge estimate, is useful for laboratory and field investigations. Finally, specific analysis for the triangular broad-crested weirs with p/B > 0 was developed to modify the stage–discharge relationship obtained for the case p/B = 0. This specific stage–discharge relationship allows to reduce the errors, which are generally less than ±5%, in the estimate of discharge for triangular broad-crested weirs with p/B > 0 and is also applicable for the case p/B = 0.