Assessing Experimental Relationships and Numerical Modeling for Predicting Discharge Coefficient of Rectangular Piano Key Weirs using Response Surface Methodology

This study examines the hydraulic relationships provided for piano-key weirs. The hydraulic relationships presented by researchers in various sources include multiple geometric parameters in some cases, while others focus only on a limited number of these parameters. In the first step, using the RSM-CCD method and data from Anderson's study (2011), the discharge coefficient relations were derived in the relative head ranges of 0.1-0.2 and 0.2-0.9, with a total of 18 data points. In the second step, through laboratory and numerical model designs, the derived relationship using the RSM-CCD method was compared and evaluated against other hydraulic relationships for piano-key weirs. This comparison was done using statistical indices and the discharge-head ratio charts. The statistical index values obtained from generalizing the discharge coefficient relation using the RSM-CCD method to Anderson's (2011) 115 laboratory data points were R² = 0.9985, MAE = 0.0034, and RMSE = 0.0041, indicating the accuracy of this method, despite using fewer data points. Evaluation of the hydraulic relationships presented for predicting the discharge coefficient of the physical model of the studied piano-key weir, using statistical indices, shows the good performance of the relationships by Liet-Ribeiro et al. (2012) and Michaels (2012). The R², MAPE, and RMSE values for these two relationships are 0.99, 5.05%, 0.063, and 0.96, 6.8%, 0.071, respectively. Comparison of the discharge-head ratio charts derived from the RSM-CCD method and laboratory models shows that the accuracy of this relationship increases with increasing relative flow head. The MAPE values for the relative head ranges of 0.1-0.3 and 0.3-0.8 were 11% and 1.25%, respectively, which can be considered when predicting discharge at high relative heads.