Modified discharge capacity calculation method for piano key weirs

Due to the numerous geometric parameters and complex hydraulic behaviors of piano key weirs (PKWs), accurately estimating their discharge capacity remains challenging without in-depth experimental studies or computational modeling. This study compares and analyzes recent discharge equations and develops new relationships between key parameters influencing the discharge capacity of PKWs, including the weir height P, weir width W, and effective crest length L. A modified theoretical discharge equation is proposed, derived from dimensional analysis and supported by existing experimental data. The calculated values from the equation agree well with the earlier experimental and the prototype observation results. For the relative water head H/P range from 0.1 to 1.5, the mean absolute percentage error remains below 8%. The proposed modified discharge method offers high accuracy and a simple form, providing a more precise description of the influence of PKW geometric parameters on discharge capacity, making it highly practical for engineering applications.