Abstract
In this paper, the stage-discharge equation of a harmonic plane weir 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 laboratory measurements carried out by Yildiz et al. (2024), a new relationship for estimating Cd is proposed. This new empirical expression of the discharge coefficient (Eq. (15)) allows for improving the performance of the stage-discharge equation (Eq. 13), which is characterized by errors in the discharge estimate E varying from – 7.7 to 7.7 % and a mean square error MSE of 0.214. Then, applying the dimensional analysis, a new stage-discharge relationship was deduced and calibrated using the same dataset. This theoretical equation is characterized by errors E ranging from – 7.1 to 7.4 %, and a MSE of 0.193. In conclusion, the stage-discharge relationship deduced by dimensional analysis is characterized by the best performances in the discharge estimate and has also the advantage of working without the need of estimating the discharge coefficient.
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