The stage-discharge relationship of a sharp-crested triangular weir pierced by square orifices

In this paper, the stage-discharge equation of a sharp-crested triangular weir pierced by square orifices is deduced applying both the classical approach of the discharge coefficient Cd and the Π- Theorem of dimensional analysis and the self-similarity theory. At first, using the experimental data by Zeinivand et al. (2024), the applicability of the expression of the discharge coefficient proposed by these authors was verified. Then, applying the dimensional analysis, a new stage-discharge relationship was deduced and calibrated using the available dataset. This theoretical equation is characterized by errors in the discharge estimate that are less than or equal to ±20 % for 98.9 % of cases and ≤ ±10 % for 87.8 % of cases, and the root mean square error is equal to 0.00071 m3 s−1. In conclusion, the stage-discharge relationship deduced by dimensional analysis is characterized by an improvement in the performances in the discharge estimate and also has the advantage of working without the need of estimating the discharge coefficient.