In this work experimental and numerical investigations were carried out to study the influence of the geometric parameters of trapezoidal–triangular labyrinth weirs (TTLW) on the discharge coefficient, energy dissipation, and downstream flow regime, considering two different orientations in labyrinth weir position respective to the reservoir discharge channel. To simulate the free flow surface, the volume of fluid (VOF) method, and the Renormalization Group (RNG) k-ε model turbulence were adopted in the FLOW-3D software. The flow over the labyrinth weir (in both orientations) is simulated as a steady-state flow, and the discharge coefficient is validated with experimental data. The results highlighted that the numerical model shows proper coordination with experimental results and also the discharge coefficient decreases by decreasing the sidewall angle due to the collision of the falling jets for the high value of H/P (H: the hydraulic head, P: the weir height). Hydraulics of flow over TTLW has free flow conditions in low discharge and submerged flow conditions in high discharge. TTLW approximately dissipates the maximum amount of energy due to the collision of nappes in the upstream apexes and to the circulating flow in the pool generated behind the nappes; moreover, an increase in sidewall angle and weir height leads to reduced energy. The energy dissipation of TTLW is largest compared to vertical drop and has the least possible value of residual energy as flow increases.

Weirs are a commonly used system to adjust water surface level and to control the flow in canals and hydraulic structures. Labyrinth weirs are a type of weirs that can pass through a certain amount of flow which has a lower upstream water level than the linear weirs, by increasing the effective length. In the present study, the performance of multilayer perceptron (MLP) networks, radial basis function networks and support vector machines with different kernel functions were investigated in order to estimate the discharge coefficient (C_d) of labyrinth weirs with quarter-round crests. For this purpose, 454 laboratory data were used. The non-dimensional parameters of L/W, a, W/P, and H_t/P were considered as the input, and the non-dimensional parameter of C_d was regarded as the output in the models. In comparison with the other models, the performance of the MLP model with RMSE, R, and DC of 0.019, 0.985, and 0.971, respectively, was more acceptable and closer to the experimental data. Also, the data density plot and the violin plot showed that the dispersion and distribution of the probability of the estimated data to the MLP model with the data obtained from the laboratory have a very close and similar adaptation.

This study investigates experimentally and numerically the effects of sills with different geometric specifications at various positions on the hydraulic characteristics of flow through sluice gates. The simulation results showed that the RNG turbulence model’s statistical indicators yield high accuracy compared to the k-ε, k-ω, and LES turbulence models. The discharge coefficient (C_d) has an inverse relationship with gate opening. Regarding sill state, the discharge coefficient is higher than no-sill state. In the case of non-suppressed sills, the C_d decreases compared to the smaller openings as the opening of the gate changes. The results showed that the C_d with a sill in the tangent position upstream of the gate is higher than the downstream tangent and below situations. Increasing the sill length leads to an increase in flow shear stress and consequently a decrease in C_d. The C_d of gates with different sill thicknesses is always higher than the no-sill state, but due to the constant ratio of the fluid depth above the sill to the gate opening, the C_d increases to a certain extent and then decreases with increasing sill thickness.

In the present study, the performance of the support vector machine for estimating vertical drop hydraulic parameters in the presence of dual horizontal screens has been investigated. For this purpose, 120 different laboratory data were used to estimate three parameters of the drop: the relative length, the downstream relative depth, and the residual relative energy in the support vector machine. For each parameter, 12 models were analyzed by using a support vector machine. The performance of the models was evaluated with statistical criteria (R2, DC, and RMSE) and the best model was introduced for each of the parameters. The evaluation criteria for the relative length of the vertical drop equipped with dual horizontal screens for the testing stage are R2 = 0.992, DC = 0.981 and RMSE = 0.050. Also, the values of the downstream relative depth evaluation indicators for the testing stage are R2 = 0.9866, DC = 0.980 and, RMSE = 0.0064. For the residual relative energy parameter, the values of the residual relative energy evaluation indicators are R2 = 0.9949, DC = 0.9853 and RMSE = 0.0056. The results showed the capacity for this approach to predict the hydraulic performance of these systems with accuracy.

This investigation focuses on flow energy, a crucial parameter in the design of water structures such as channels. The research endeavors to explore the relative energy loss (ΔEAB/EA) in a constricted flow path of varying widths, employing Support Vector Machine (SVM), Artificial Neural Network (ANN), Gene Expression Programming (GEP), Multiple Adaptive Regression Splines (MARS), M5 and Random Forest (RF) models. Experiments span a Froude number range from 2.85 to 8.85. The experimental findings indicate that the ΔEAB/EA exceeds that observed in a classical hydraulic jump with constriction section. Within the SVM model, the linear kernel emerges as the best predictor of ΔEAB/EA, outperforming polynomial, radial basis function (RBF), and sigmoid kernels. In addition, in the ANN model, the MLP network was more accurate compared to the RBF network. The results indicate that the relationship proposed by the MARS model can play a significant role resulting in high accuracy compared to the non-linear regression relationship in predicting the target parameter. Upon comprehensive evaluation, the ANN method emerges as the most promising among the candidates, yielding superior performance compared to the other models. The testing phase results for the ANN-MLP are noteworthy, with R = 0.997, average RE% = 0.63%, RMSE = 0.0069, BIAS = −0.0004, DR = 0.999, SI = 0.0098 and KGE = 0.995.

Experimental tests were carried out to investigate the effective scouring parameters downstream from stepped spillways with different flow rates and step sizes. The results indicated that the flow regime plays an important role in scour-hole dimensions such that the minimum scouring depth happens in the nappe flow regime. Moreover, step size and tailwater depth are essential parameters for maximum scouring depth. Increasing tailwater depth from 6.31 cm to 8.54 cm and then to 11.82 cm decreases the scouring depth by 18.56% and 11.42%, respectively. These alterations also decrease the scouring length by 31.43% and 16.55%, respectively. By increasing the flow rate, the particle Froude number will increase, and the increased momentum of the flow promotes scouring. In addition, the results show that scouring at the sidewalls is higher than in the middle of the cross-section. Finally, an empirical formula with root mean square error = 0.107 and R2 = 0.974 is proposed to predict the maximum scouring depth downstream from the stepped spillways. Comparisons were made between the proposed formula and experimental results. This comparison demonstrated that the formula can predict souring depth to within 3.86% and 9.31% relative and maximum errors, respectively.