Experimental Study on Piano Key Weirs of an Ogee Outlet Key for Enhancement in Discharge Capacity

The Piano Key Weir (PKW) has emerged as an effective solution for enhancing the discharge capacity of spillways, particularly in low-head dams. This study presents an experimental investigation comparing two Type A PKW models that differ solely in the geometry of their outlet keys: linear (L-PKW) and curvilinear ogee (CL-PKW). Laboratory tests were conducted under free-flow conditions, and H/P ratios (where H is the upstream head above the crest and P is the weir height) between 0.17 and 0.63 were analyzed in detail. The results suggest that CL-PKW shows improved discharge efficiency relative to L-PKW, with observed increases ranging from 12.4% to 18.1% across the tested conditions. The curvilinear ogee outlet key, derived from the Waterways Experiment Station (WES) standard spillway profile and fabricated as a smooth, curved slab, reduces nappe interference and flow separation, contributing to a higher discharge coefficient. A novel empirical equation was developed using 90 data points, including results from the present study and previous literature, to predict the discharge coefficient of Type A PKWs with both outlet key types. Comparative analysis with existing equations indicates that the proposed equation provides predictive accuracy comparable to, and in some cases slightly better than, established formulations, with 88% and 100% of data points falling within 9% and 12% absolute error bounds, respectively. The proposed equation also exhibited lower root mean squared error (RMSE) and mean absolute percentage error (MAPE) values, indicating a predictive performance that is comparable to, and in some cases modestly better than, existing empirical equations for different outlet geometries and flow conditions. By addressing the overlooked influence of outlet key geometry, this study fills a critical research gap and introduces a versatile tool for discharge prediction. The findings offer practical guidance for hydraulic engineers in the design and optimization of PKWs for spillway improvements and dam safety upgrades.