A Reformed Empirical Equation for the Discharge Coefficient of Free-Flowing Type-A Piano Key Weirs

The existing equations for the discharge coefficient of Piano key weirs (PKWs) use a limited range of experimental data, which means that they are inappropriate for wide parametric ranges that might lead to significant errors. This study aimed to propose a reformed empirical equation using a wide range of data points gathered from previous experimental studies. Further, the appropriateness to use the existing equations for the collected data points, and the related errors, were investigated in detail using graphical and statistical analyses. The proposed equation predicted the discharge coefficients with < 5% absolute errors for 83.5% data points and with < 10% absolute errors for 100% data points, and the mean absolute error was 2.9%. Such variations may be attributed to the differences in experimental conditions that exist among the previous studies. The correlation indices were higher for the proposed equation as compared to the same for the existing equations, whereas the error indices were lowest for the proposed one. For some very specific parametric ranges, the existing equations still hold better accuracy. Overall, the proposed equation can precisely estimate the discharge coefficient of the basic geometry of Type-A PKWs for a wide parametric range and will be handy in the hydraulic design of such PKWs.

Automated summary

This study proposed an empirical equation for the discharge coefficient of Piano Key Weirs (PKWs) using a wide range of data points collected from previous experimental studies. The appropriateness of existing equations for the collected data points and the related errors were investigated through graphical and statistical analyses. The proposed equation predicted discharge coefficients with high accuracy for a wide range of parametric conditions, making it useful in hydraulic design.