Literature-Based Empirical and Data-Driven Model Evaluation of Labyrinth Side Weir Flow Coefficients under Different Geometric and Hydraulic Conditions

This study comprehensively investigated the hydraulic behavior of labyrinthine side weirs in open channels using newly developed statistical approaches based on experimental data compiled from the literature. The model used in this study is a multiple linear regression model. The main objective was to reveal the complex relationships between the discharge coefficient (Cd) and the dimensionless flow parameters and the discharge. Experimental data showed that Cd values exhibit a nonlinear relationship with the flow regimes, which is characterized by the dimensionless h/w ratio with the optimal hydraulic performance region being h/w=2.0−2.6. Furthermore, a general decreasing trend in Cd was observed as the discharge (Q) increased, with a particularly dramatic decrease at high flow rates above 10 L/s, indicating potential choking effects at high discharges. A model was developed to estimate the flow coefficients using SPSS statistical software. While this model successfully captured the general trends, it showed significant deviations from the experimental data in certain flow regimes. Regression analyses revealed that the model can predict with high accuracy in low and medium-high flow rate ranges (e.g., R2=0.91 for 6-8 L/s, R2=0.95 for 11-12.5 L/s), but that there is a significant decrease in predictive power at very high flow rates (R2=0.70 for 17-23 L/s). These findings point to limitations in the generalizability of the model and the need for more sophisticated modeling approaches, especially for the complex flow dynamics in high flow regimes. Regression analyses showed that the model performed with high accuracy in medium flow ranges (R2=0.91 and R2=0.95), but its predictive power decreased at high flow rates (R2=0.70). These findings contribute to the hydraulic design of labyrinth weirs and underscore the need for advanced predictive tools in high-flow scenarios. The obtained data provide significant contributions to the hydraulic design principles of labyrinth weirs and provide a scientific basis for the development of more effective and reliable tools for water resources engineering applications.