Introduction

Piano key weirs (PKWs) are increasingly used as efficient spillway structures due to their ability to significantly increase discharge capacity without requiring an increase in dam crest width. This advantage makes them particularly suitable for dam rehabilitation and for sites where spillway expansion is constrained by topographic or structural limitations. Among different PKW configurations, Type‑A piano key weirs have received considerable attention because of their favorable hydraulic performance and structural simplicity. Despite extensive research on PKWs, the influence of geometric modifications—especially the inclination of side walls and their orientation relative to the flow direction—has not been sufficiently investigated. Side‑wall geometry can affect the flow pattern entering the inlet keys, the formation of separation zones, and the overall hydraulic efficiency of the spillway. Understanding these effects is essential for optimizing PKW performance. Therefore, the present study experimentally investigates the hydraulic behavior of Type‑A piano key weirs with different side‑wall inclinations and orientations. In addition, data‑driven models are employed to predict the discharge coefficient and evaluate the capability of machine‑learning techniques in modeling complex nonlinear hydraulic relationships.

Materials and Methods

The present study was conducted using a laboratory experimental setup designed to investigate the hydraulic performance of Type A piano key weirs under controlled flow conditions. The experiments were carried out in a rectangular flume with a constant width and adjustable discharge system that allowed accurate control of flow rates. Two geometric configurations of piano key weirs were tested: rectangular and trapezoidal inlet–outlet key shapes. The main objective was to evaluate how the inclination and orientation of the side walls influence the hydraulic efficiency and discharge coefficient of the structure.

Side wall inclination angles of 5°, 7.5°, and 10° were selected based on common ranges used in hydraulic structures and previous studies on PKW optimization. For each inclination angle, two orientations were considered: inclination with the flow direction and inclination against the flow direction. These configurations allowed the evaluation of how flow alignment and entrance conditions affect discharge characteristics. During the experiments, the upstream water head was carefully measured using precise point gauges, while the flow discharge was controlled and monitored using calibrated flow measurement devices.

The discharge coefficient (C_d) was calculated for each experimental condition to quantify the hydraulic performance of the tested configurations. The collected dataset was then used for developing predictive data driven models. Several machine learning algorithms were employed, including Artificial Neural Networks (ANN), Extreme Gradient Boosting (XGBoost), Random Forest, and Support Vector Regression (SVR). The input parameters consisted of hydraulic and geometric variables such as upstream head and side wall inclination characteristics, while the output variable was the discharge coefficient.

Model performance was evaluated using common statistical indicators including the coefficient of determination (R^2), root mean square error (RMSE), and mean absolute error (MAE). These indicators were used to assess the accuracy and reliability of each model and to determine the most suitable approach for predicting PKW discharge performance

Results and Discussion

The experimental results clearly demonstrate that the inclination and orientation of side walls significantly influence the hydraulic performance of Type A piano key weirs. Flow observations indicated that the side wall geometry directly affects the way water enters the inlet keys and how the flow is distributed along the crest. When the side walls were inclined against the flow direction, the incoming water was guided more effectively toward the inlet openings. This configuration improved the alignment of streamlines and reduced the formation of recirculation zones near the inlet edges. As a result, flow contraction and energy losses were reduced, leading to an increase in the discharge coefficient.

In contrast, when the side walls were inclined with the flow direction, the inflow pattern tended to produce local separation zones near the entrance of the inlet keys. These separation regions reduced the effective flow area and caused additional energy dissipation. Consequently, the discharge coefficient obtained in these cases was generally lower than that of the opposite orientation.

The influence of the inclination angle was also evident in the experimental data. Increasing the side wall inclination from 5° to 7.5° and 10° generally improved hydraulic performance, particularly when the inclination was directed against the flow. Among the tested configurations, the best hydraulic behavior was observed for trapezoidal models with side wall inclinations between 7.5° and 10° oriented against the flow direction. These configurations provided the most favorable flow guidance and minimized hydraulic disturbances near the inlet region.

A comparison between the two tested geometries showed that trapezoidal PKWs consistently produced higher discharge coefficients than rectangular ones under similar hydraulic conditions. The trapezoidal configuration appears to facilitate smoother flow transitions and better distribution of water across the inlet keys, which enhances the overall discharge efficiency. In some cases, the improvement in discharge coefficient reached approximately 15% compared with the corresponding rectangular configurations.

The data driven modeling results further confirmed the experimental findings. Among the applied machine learning techniques, Artificial Neural Networks (ANN) and Extreme Gradient Boosting (XGBoost) showed the best predictive capability. These models successfully captured the nonlinear relationships between geometric parameters and hydraulic performance. The predictive accuracy of these models exceeded 98%, while the associated prediction errors remained below 2%, indicating excellent agreement with the experimental measurements.

The results highlight the effectiveness of combining experimental investigations with modern machine learning techniques to better understand and predict the hydraulic performance of complex spillway structures such as piano key weirs.

Conclusions

This study investigated the effects of side wall inclination and orientation on the hydraulic performance of Type A piano key weirs using laboratory experiments and data driven modeling. The results showed that inclining the side walls against the flow direction significantly improves flow alignment and reduces energy losses, resulting in higher discharge coefficients. Trapezoidal configurations demonstrated superior performance compared with rectangular geometries, with improvements reaching approximately 15%. Machine learning models, particularly ANN and XGBoost, provided highly accurate predictions of the discharge coefficient. The findings provide useful guidance for optimizing PKW design and demonstrate the value of integrating experimental data with advanced predictive modeling techniques.

The study contributes a validated experimental dataset and robust machine learning formulations that can assist designers in optimizing PKW configurations for enhanced hydraulic efficiency and safer spillway design.