Assessing the stage-discharge relationship of streamlined-type weirs

The flow stage-discharge relationship (SDR) of weirs is a well-studied hydraulic topic that is generally concerned with energy considerations and using a discharge coefficient. In this context, dimensional analysis and self-similarity theory are alternative theoretical methods to obtain accurate stage-discharge curves. In this paper, the SDR of streamlined-type weirs (streamlined SLW, hydrofoil HW, and modified semi-cylindrical MSCW) is theoretically deduced using dimensional analysis and the self-similarity condition. These new SDRs are estimated using experimental results from the literature. For the SLW, the analysis demonstrated that the new SDR gives discharge estimates similar to those obtained by the theoretical equation proposed by Carollo and Ferro (2021). For the HW, the SDR, calibrated by the measurements of Soydan Oksal et al. (2021), results in errors always less than the accuracy limit of ±5 %. Furthermore, for the same geometric parameters and upstream water level, the analysis pointed out that a HW flows a discharge higher than that corresponding to a SLW. For the MSCW, the SDR, calibrated by the measurements of Afaridegan et al. (2023), results in errors lower than or equal to ±3 % in 95.6 % of cases. Thereby, for SLW, HW, and MSCW, the developed analysis showed that the proposed SDR results in errors in discharge estimates always less than those obtained for the literature solutions. Finally, a single SDR, useful for all streamlined-type weirs, was also determined, and it results in errors lower than or equal to ±5 % for 96.1 % of cases and lower than or equal to ±3 % for 76.6 % of cases.