An Extra Tree Regression Model for Discharge Coefficient Prediction: Novel, Practical Applications in the Hydraulic Sector and Future Research Directions

Despite modern advances used to estimate the discharge coefficient ( C d ), it is still a major challenge for hydraulic engineers to accurately determine C d for side weirs. In this study, extra tree regression (ETR) was used to predict the C d of rectangular sharp-crested side weirs depending on hydraulic and geometrical parameters. The prediction capacity of the ETR model was validated with two predictive models, namely, extreme learning machine (ELM) and random forest (RF). The quantitative assessment revealed that the ETR model achieved the highest accuracy in the predictions compared to other applied models, and also, it exhibited excellent agreement between measured and predicted C d (correlation coefficient is 0.9603). Moreover, the ETR achieved 6.73% and 22.96% higher prediction accuracy in terms of root mean square error in comparison to ELM and RF, respectively. Furthermore, the performed sensitivity analysis shows that the geometrical parameter such as b/B has the most influence on C d . Overall, the proposed model (ETR) is found to be a suitable, practical, and qualified computer-aid technology for C d modeling that may contribute to enhance the basic knowledge of hydraulic considerations.

Discharge Calculation of Side Weirs with Several Weir Fields Considering the Undisturbed Normal Flow Depth in the Channel

Discharge behavior at side weirs is significantly influenced by the water surface profile along the weir crest. In the past century, different approaches were developed to describe this profile and the associated discharge coefficients. However, the application of these methods to practical problems poses a particular challenge, as a complex three-dimensional funnel is formed due to the discharge reduction, leading to significant uncertainties in determining the relevant flow depth. For this reason, a new approach for the determination of the discharge coefficient of side weirs was developed that refers to the undisturbed normal flow depth in the main channel. Based on a comprehensive parametric study utilizing 3D-numerical simulations, the influence of the weir and channel characteristics on the discharge behavior at the side weir was analyzed. A revised formula for estimating the discharge coefficient for side weirs with multiple weir fields was derived using multiple regression analyses. Validation of the numerical simulations was carried out by applying a physical scale model, showing good agreement between the results.

The Effect of Geometric Parameters of the Antivortex on a Triangular Labyrinth Side Weir

Side weirs are important structural measures extensively used, for instance, for regulating water levels in rivers and canals. If the length of the opening is limited, the amount of water diverted out of the channel and the effective length can be increased by applying a labyrinth side weir. The present study deals with numerical simulations regarding the hydraulic performance of a labyrinth side weir with a triangular plan in single-cycle mode. Specifically, six different types of antivortexes embedded inside it and in various hydraulic conditions at different Froude numbers are analyzed. The antivortexes are studied using two groups, permeable and impermeable, with three different heights: 0.5 P, 0.75 P, and 1 P (P: Weir height). The comparison of the simulated water surface profiles with laboratory results shows that the numerical model is able to capture the flow characteristics on the labyrinth side weir. The use of an antivortex in a triangular labyrinth side weir reduces the secondary flows due to the interaction with the transverse vortexes of the vertical axis and increases the discharge capacity by 11%. Antivortexes in a permeable state outperform those in an impermeable state; the discharge coefficient in the permeable state increases up to 3% with respect to the impermeable state. Finally, based on an examination of the best type of antivortex, taking into account shape, permeability, and height, the discharge coefficient increases to 13.4% compared to a conventional labyrinth side weir.

Experimental study and performance comparison on various types of rectangular piano key side weirs at a 120° section of a 180° curved channel

Application of side weirs with high effective length is necessary to discharge excessive flows, to control the flow in water conveyance systems, and irrigation and drainage systems. Most of the studies on the side weirs have been conducted on the straight channels and linear weirs. The flow pattern on the outer arc of the curved channels and its suitability for side weir can be used and combined with the piano key weirs. So far, no comparison has been made on rectangular piano key side weirs (RPKSW) at a 120° Section of a 180° Curved Channel. In this study, an experimental study was performed on A-, B-, C-, and D-type RPKSW at a bend angle of 120 degrees. The results showed that the specific energy at two ends of the RPKSWs was the same, with a slight difference of 3.4% for A-Type, 1.3% for B-Type, 1.1% for C-Type, and 1.8% for D-Type weirs. The discharge coefficients of the studied weirs were also investigated, and it was concluded that B-Type weir has better performance than other weirs. On average, the discharge coefficient of B-Type weir was 9.9%, 21.2%, and 24.1% higher than that of A-Type, C-Type, and D-Type weir, respectively. It was shown that the ratio of P/h1 is the main parameter affecting the weir discharge coefficient. Finally, an empirical equation was proposed for each weir. The proposed equation has MAE = 0.028 for A-Type weir, MAE = 0.041 for B-Type weir, MAE = 0.049 for C-Type weir, and MAE = 0.053 for D-Type weir.