A Master’s thesis by researcher Muhannad Rahman Ba’ir was defended at the University of Basrah’s College of Engineering (Department of Civil Engineering), under the supervision of Professor Dr. Saleh Issa Khassaf. The thesis is titled: Experimental study of the hydraulic performance for piano key weir with different crest shapes

Piano Key Weirs (PKWs) have emerged as an efficient alternative to conventional weirs due to their ability to increase discharge capacity without requiring additional spillway width. However, the hydraulic performance of PKWs is strongly influenced by crest geometry and flow conditions. Therefore, this study experimentally and numerically investigated the influence of different inlet and outlet crest configurations on the hydraulic performance of PKWs under both free-flow and submerged-flow conditions.
Nine PKW models (S1–S9) with different inlet and outlet geometries, including flat, semi-circular, quadrant, triangular, and zigzag configurations, were fabricated and tested in a 15 m long, 0.30 m wide, and 0.45 m deep laboratory flume. The experiments were conducted under discharge conditions ranging from 12.91 to 30.58 L/s. The hydraulic performance was evaluated using the discharge coefficient (C_dW) under free-flow conditions and the discharge reduction coefficient (C_s) under submerged-flow conditions. Furthermore, a comprehensive numerical investigation was performed using FLOW-3D software to simulate the complex three-dimensional free-surface flow behavior and validate the experimental observations.
The experimental results demonstrated that the discharge coefficient generally decreased with increasing relative head ratio (H_0/P) for all tested configurations. Under free-flow conditions, Model S8 (zigzag half-circle inlet–outlet) achieved the highest hydraulic efficiency with an average discharge coefficient of 2.252, representing an improvement of 8.62% compared with the reference flat–flat configuration (S1). Model S7 (Zigzag (Rectangular) – Zigzag (Rectangular)) ranked second with an improvement of 2.87%, whereas Models S2 and S9 exhibited slightly lower performance than the reference model due to increased flow separation and turbulence associated with triangular crest geometries.
Under submerged-flow conditions, the discharge reduction coefficient decreased progressively with increasing submergence factor (Sⓜ=H_d/H_u ), indicating the significant influence of downstream tailwater on hydraulic efficiency. Among the tested configurations, Model S6 (triangle–triangle) exhibited the highest average performance with Cs = 0.657, corresponding to an improvement of 3.79% over the reference model. In contrast, Model S8 recorded the lowest average performance (Cs = 0.594), indicating greater sensitivity to submergence effects.
An empirical equation was developed using dimensional analysis and nonlinear regression techniques to predict the discharge coefficient under free-flow conditions. The proposed model showed excellent agreement with the experimental data, yielding a coefficient of determination (R²) of 0.928, RMSE of 0.081, MAE of 0.062, and MAPE of 2.97%. A second empirical relationship was also developed for predicting the discharge reduction coefficient under submerged-flow conditions, providing reliable estimates across the investigated range of operating conditions.
The numerical simulations successfully reproduced the experimental hydraulic behavior under both free-flow and submerged-flow conditions. The FLOW-3D model accurately predicted velocity distributions, pressure fields, free-surface profiles, turbulence characteristics, and discharge coefficients. Statistical validation demonstrated excellent agreement between experimental and numerical results, with prediction errors generally below 5% and a coefficient of determination reaching R² = 0.989 under submerged-flow conditions.
The findings confirm that crest geometry plays a fundamental role in controlling PKW hydraulic performance. Smooth curved and optimized zigzag configurations significantly improve free-flow discharge capacity, whereas triangular inlet–outlet arrangements provide superior performance under submerged-flow conditions. The developed empirical equations and validated numerical model provide practical design tools for predicting PKW hydraulic efficiency and optimizing future spillway configurations.