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Piles are walls that are installed underneath hydraulic structures to control seepage flow, uplift pressure, and exit hydraulic gradient. In this study, the effect of the ratio of width of the apron to the foundation depth (B/D), the ratio of the width of the apron to the downstream pile depth (B/d2), and the ratio of the upstream and downstream pile depths (d1/d2) on seepage flow characteristics is numerically investigated using the finite-element method. From the numerical simulations, design charts, and explicit formulas for estimating seepage flow characteristics, such as the percentage residual uplift pressure at key points, the discharge flow factor, and the exit hydraulic gradient factor underneath aprons with end double-piles for both states of equal and unequal depths are developed. The simulations are validated with existing analytical solutions for simple cases. To assess the accuracy of the presented formulas, statistical metrics; that is, the determination coefficient, root mean square error, and percent relative error (RE%) were used. The statistical metrics are satisfactory, and their values quantified the reliability of the proposed formulas. The proposed explicit formulas, with RE% less than 5%, could be used by design engineers instead of implicit analytical equations that involve elliptic integrals. [ABSTRACT FROM AUTHOR]

The effects of geometrical parameters (crest height, number of cycles, and plan weir configuration), are investigated experimentally on labyrinth weirs, over a range of headwater ratios of 0.1 to 0.6. Trapezoidal and triangular weirs have a constant angle α=15° , whereas rectangular weirs have the same footprint size B as the trapezoidal configuration. Data uncertainties are quantified at a relatively small overall average of 1.88%. For taller labyrinth weirs, current experimental models achieve lower discharge coefficients when all other geometrical parameters are kept the same. Increasing the number of cycles also leads to a reduction in flow rate and discharge coefficient. These hydraulic performance reductions were most significant for trapezoidal followed by rectangular and triangular configurations. For the same geometrical conditions, a rectangular configuration had a higher flow rate for each head, followed by trapezoidal and then triangular. Nappe behaviors were significantly different between the configurations, whereas modifying the geometrical ratios had less significant effects on the flow characteristics of each configuration. [ABSTRACT FROM AUTHOR]

We note that Rady ([4]) also investigated these type of gates for HT ht . (4) and (7), there is no gate inclination angle ( HT ht ). (6) and (7) without knowledge about HT ht or HT ht . In determining HT ht , Figs. [Extracted from the article]

Weirs are commonly used for making discharge measurements in irrigation canals. There are several types of weirs that are categorized based on their geometric shape or hydraulic properties. A gabion weir is a porous weir that can pass flow through its body in addition to the flow that passes over the weir. This study focuses on determining the discharge coefficients (Cd) for rectangular broad-crested gabion weirs using fabricated physical models. Dimensional analysis was carried out for finding the most effective parameters that govern the flow. Results show that the Cd of gabion weirs is 10.5% greater than that of similar solid weirs. In addition, the Cd for porous weirs in free flow conditions is 17.2% greater than that for submerged flow. For H/L>0.45 (where H is the water depth over the weir crest and L is the weir length) a porous weir acts similar to a solid weir and the effect of porosity (n) nearly vanishes. For a specified value of H/L , the ratio of submergence (Sr) for a solid weir is higher than that for porous weirs. Porous weirs with 50% porosity have lower values of Sr compared with solid weirs and weirs with lower porosities, of 45%, 41%, and 30%. Regression equations for the flow through gabion weirs were generated for free and submerged flow conditions. The derivations of equations were carried out using multivariable nonlinear regression and genetic programming (GP). Finally, a comparison of Cd in the present study with the other studies was carried out. [ABSTRACT FROM AUTHOR]

Slide gates are commonly used to adjust flow in open canals. The discharge coefficient (Cd) for a slide gate is a function of the gate's geometric and hydraulic characteristics. For free flow conditions, Cd depends on the upstream water level and the opening of the gate, whereas for submerged flow, it also depends on the downstream water level. The main aim of this study is to conduct a series of laboratory experiments to determine Cd for inclined slide gates. These tests and models were used to evaluate both free and submerged flows. Experiments with inclination angles of 0°, 15°, 30°, and 45° were studied with different gate openings. The collected data are used to develop equations for predicting Cd. The results show that the inclination of the slide gates has a progressive effect on Cd and increases capacity under the gate. The increase in Cd relates to the convergence of the flow through the gate opening. The produced equation via genetic programming with R2 and a relative error of 0.9431 and 0.0014 had optimal efficiency compared with classical multiple regression models. A comparison with other studies for inclination angles of 45° and 60° was also conducted. [ABSTRACT FROM AUTHOR]

In this study, a numerical simulation is applied to investigate the effective factors on the seepage from the earthen channels. To authenticate the information at hand, some of the earthen channels in the Zayandeh-Rud irrigation network in Iran and Gediz watershed in Turkey were studied. 246 numerical models, including different sections of trapezoidal, rectangular and triangular earthen channels, were performed using the finite elements method (FEM). The results showed that, for a numerical simulation, a width of 15 times wider than the top width of the water surface in the channel would be required for the modelling of the left and right lateral boundaries. The comparison of the seepage with empirical relationships showed that the empirical relationships have too much error in the seepage estimation, however, Moritz's relation with the coefficient of determination (R2) of 0.373 was better than the others. The linear and nonlinear multivariate regression relationships provide a suitable match for the seepage discharge estimation. The wetted perimeter has been distinguished as an effective parameter in the seepage from the channels, yet the channels side slope has a low impact on the seepage. [ABSTRACT FROM AUTHOR]

(11), (12), (14), and (15) included weir length ( HT ht ) and weir height ( HT ht ). 2 in the discussion calculates the discharge coefficient ( HT ht ) for that part of the flow that passes only through the porous gabion weir. The theory developed by the discusser is new and separates flow into weir overflow and weir through flow. It should be noted that the main purpose of the writers' article was to determine the discharge coefficient for gabion weirs and not that for impermeable/solid weirs. [Extracted from the article]

In a stepped spillway, the spillway face is provided with a series of steps from near the crest to the toe. The energy dissipation caused by the steps reduces the size of the energy dissipator, generally provided at the toe of the spillway. The hydraulics of stepped spillways is investigated by carrying out laboratory experiments, building models to explain the data, and testing the robustness of the models developed here using a neuro-fuzzy approach. The experiments consist of twenty different stepped spillways tested in a horizontal laboratory flume, a wide range of discharge values, three weir slopes of 15°, 25°, and 45° and different step numbers from 3 to 50 on the ogee surface. The main objective of this paper was to investigate the applicability and accuracy of the neuro-fuzzy approach in estimating the proper values of energy dissipation of skimming flow regime over stepped spillways because of the imprecise, insufficient, ambiguous and uncertain data available. A neuro-fuzzy approach was developed to relate the input and output (energy dissipation) variables. Multiple regression equations based on dimensional analysis theory were developed for computing energy dissipation over stepped spillways. The determination coefficients for the suggested neuro-fuzzy model in training and testing process are 0.974 and 0.966, respectively. It was found that the neuro-fuzzy approach formulation of the problem of solving for the energy dissipation over stepped spillways is more successful than that by regression equations. [ABSTRACT FROM AUTHOR]

In this study, different physical models of stepped spillways are constructed and the effect of intense water mixing on increasing the dissolved oxygen concentration in water is investigated. The minimum oxygen transfer efficiency ranged from 28% to 56%, which indicates the positive effects of stepped spillways. The results showed that with a stepped spillway, the oxygen transfer efficiency decreases with increasing discharge. As the discharge increases and all steps become submerged, the effect of the spillway steps on the turbulence and aeration of the flow decreases. At high unit discharges (more than 0.15 m2/s), aeration efficiency increases with increasing spillway slope. However, for discharges less than 0.15 m2/s, the effect of slope on aeration efficiency is negligible. This stepped spillway performance indicates that in the nappe regime, the effect of slope on the aeration efficiency is less than for the skimming regime. A number of nonlinear regression equations are presented to estimate aeration efficiency. • The dissolved oxygen concentration in water is investigated in stepped spillways. • The minimum oxygen transfer efficiency was 28% and the maximum was 56%. • In a stepped spillway, the oxygen transfer efficiency decreases with increasing discharge. • A number of nonlinear regression equations were presented to estimate aeration efficiency. [ABSTRACT FROM AUTHOR]

The hydraulic design and analysis of flow conditions in pipe networks are dependent upon estimating the friction factor, f . The performance of its explicit formulations and those of artificial intelligence (AI) techniques are studied in this paper. The AI techniques used here include artificial neural networks (ANNs) and genetic programming (GP); both use the same data generated numerically by systematically changing the values of Reynolds numbers, Re , and relative roughness, ∈/D , and solving the Colebrook-White equation for the value of f by using the successive substitution method. The tests included the transformation of Re and ∈/D using a logarithmic scale. This study shows that some of the explicit formulations for friction factor induce undue errors, but a number of them have good accuracy. The ANN formulation for the solving of the friction factor in the Colebrook-White equation is less successful than that by GP. The implementation of GP offers another explicit formulation for the friction factor; the performance of GP in terms of R² (0.997) and the root-mean-square error (0.013) is good, but its numerically obtained values are slightly perturbed. [ABSTRACT FROM AUTHOR]

Results of a study designed to examine the behavior of gabion-stepped weirs for energy dissipation are presented in this paper. Laboratory tests were conducted with 8 physical models consisting of 3 different porosities (38%, 40%, and 42%) and 2 slopes (1:1 and 1:2). An iron plate was also placed on each horizontal and vertical step to study and classify the effect of step porosity on the energy dissipation rate. A decision tree technique was used to derive if-then rules in order to classify the energy dissipation through the weir models. Results from this study suggest that a decision tree model has an accuracy of 85% in predicting the energy dissipation through a gabion-stepped weir using different attributes. The results demonstrate that the decision tree technique can be used as a reasonable method for classification of different parameters involved in energy dissipation through a gabion-stepped weir, and it can effectively identify the influence of various parameters on energy dissipation. [ABSTRACT FROM AUTHOR]

Gates in dams and irrigation canals are used for controlling discharge and for water regulation. To determine the discharge under a gate, the discharge coefficient (C d) must be quantified. This study investigates the effect of sill shape under a vertical sluice gate on C d. The study also includes the influence of height. The investigated shapes are comprised of polyhedral and non-polyhedral sills. Multiple nonlinear regression (MNLR) is applied to predict C d values and the results show that circular sills under the gate can increase C d by 23–31%. A circular sill with a 3 cm diameter has the highest C d and trapezoidal sills have the lowest C d. On the other hand, semicircular sills have moderate values of C d. The most influential parameters affecting C d are H 1 / p and Z / G where H 1 is the upstream head over the sill crest, p is the sill wetted perimeter, Z is the height of sill, and G is the gate opening. Using dimensionless parameters and regression analysis, an equation for predicting C d in free flow conditions with and without a sill is presented. The equation agrees with previously published results and can be implemented for predicting C d in sluice gates with and without sills to within 6% accuracy. • The effect of sill shape on discharge is studied. • Circular sills under the gate can increase C d between 23 and 31%. • Hydraulic radius, gate opening and upstream head are most influential. • Predictive equations for discharge coefficients are provided. [ABSTRACT FROM AUTHOR]

• Numerical investigation of double-cutoff walls beneath hydraulic structures. • The FEM can predict uplift force and exit hydraulic gradient with a maximum 5% error. • Decreasing the distance between the two cutoffs can reduce uplight. In the design of hydraulic structures, cutoff walls are needed to reduce uplift force (U) and the exit hydraulic gradient (G R). Usually two cutoff walls are required; an upstream cutoff wall is used to reduce the resultant of uplift force and a downstream cutoff wall is used to reduce the exit hydraulic gradient. This study numerically investigates double-cutoff walls beneath hydraulic structures with variations in their location and depth. Governing equations with specified boundary conditions are solved using the finite element method (FEM). Results show that if the downstream cutoff wall is deeper than the upstream cutoff wall, the resultant of uplift force will increase (compared to the no-cutoff wall case). With a constant hydraulic structure width (B), decreasing the distance between the two cutoffs (L), results in a reduction of uplift force. For L / B = 0.7, the change in the slope of the uplift force is large. Increases in the permeable depth (D) and reductions of B will lower the uplift forces. Increases in the downstream cutoff depth (d 2) and L result in a reduction in the exit hydraulic gradient (G R). When the two cutoffs are located at the end of the hydraulic structure, G R is lower than when the downstream cutoff wall is located at a more downstream location. Comparisons between the available analytical solutions and computational results for two equal cutoffs show that the FEM can predict U and G R with a maximum of 5% error. [ABSTRACT FROM AUTHOR]

• Seepage associated with various-shaped water channels was investigated. • Newly developed allow calculation of seepage discharge. • The analysis allows users to assess the sensitivity of seepage on various flow or geometric parameters. Seepage losses from unlined channels are a major contributor to water loss in the agricultural sector. Quantification of seepage losses can improve water conveyance efficiency and provide solutions to water scarcity. In this study, a numerical simulation method is applied to investigate the factors that affect seepage from earthen channels. SEEP/W software was used to generate finite element method (FEM) solutions of the seepage flow equations. 246 numerical models, including different sections of trapezoidal, rectangular, and triangular earthen channels were studied using FEM. Numerical results are compared to available observation data from Zayandeh-Rud irrigation channels in Iran. Non-linear regression equations for the four empirical seepage equations are obtained from the SPSS statistical software. The results show that nonlinear multivariate regression relationships provide a suitable match for estimating seepage discharge. The accuracy of the suggested nonlinear regression equation in terms of R2 and RE are 0.928 and -2.42 %, respectively. Comparison of the seepage discharge with the empirical relationships showed that the empirical relationships have excessive error. [ABSTRACT FROM AUTHOR]

An important step toward spillways design always involves appropriate determination of the discharge coefficient. Since existing equations are incapable of estimating the discharge coefficient of stepped spillway accurately, other approaches such as data driven techniques can be employed as an alternative which are useful in modeling processes when the physical knowledge is limited. For this purpose, Gene Expression Programming (GEP) and Support Vector Machine (SVM) as data driven methods were applied for the modeling discharge coefficient of the stepped spillways using data derived from physical models and original experiments under nappe and skimming flow regimes. The input parameters included different dimensionless geometric and hydraulic parameters of napped and skimming regimes data. The obtained results indicated that the applied methods have a high capability in the modeling of discharge coefficient for the stepped spillways. The model comprised of four input parameters used for modeling of the discharge coefficient in nappe flow showed more accurate results (%RMSE = 0.042, 0.328 and R 2 = 0.966, 0.961 for the SVM and GEP models, respectively). In skimming flow data, the model with five input parameters produced RMSE = 0.015, 0.357 and R 2 = 0.987, 0.979 in SVM and GEP, respectively. A comparison of the GEP and SVM results with the obtained results from the Multiple Linear Regression (MLR) showed that the performance of the linear model (i.e., MLR) was not suitable because the phenomenon of discharge coefficient is inherently complex and nonlinear. The results of sensitivity analysis for both proposed methods showed that the Fr 1 and H/y 1 parameters in nappe flow and Fr 1 and Re parameters in skimming flow had the most important influence on modeling of the stepped spillways discharge coefficient. The results also revealed that the SVM relatively surpassed the GEP in the modeling of discharge coefficient. Nevertheless, the utilization of GEP model is highly recommended due to the high performance and extracting of simple, explicit equation by it. [ABSTRACT FROM AUTHOR]

Highlights: [•] We applied ANN and GEP to predict energy dissipation over stepped spillway. [•] For both techniques 12 same models were evaluated. [•] We selected the best model for all kind of data to predict energy dissipation. [•] For nappe data, drop number is effective on energy dissipation. [ABSTRACT FROM AUTHOR]

• Broad-crested weirs with positive, negative and horizontal crest were examined by FVM. • Sloping the crest has a positive effect on increasing the discharge coefficient (C d). • The negative sloped crest more increases the C d than a positive sloped crest. • C d for negative sloped crest increases of 8% respect to positive sloped crest. Weirs are commonly used for controlling, measuring, and regulating water flow in conveyance structures such as canals or dams. In this study, hydraulic properties of flow over broad-crested weirs including the effects of different sloping crests and upstream and downstream ramps were characterized by using the finite volume method. Numerical simulations were validated by experimental results; the numerical simulations are very similar to the experimental results. The discharge coefficient (C d) for the broad-crested weir with upstream and downstream ramps and positive slope of crest (BCW-UDR-PSC) and the broad-crested weir with upstream and downstream ramps and negative slope of crest (BCW-UDR-NSC) are higher than the broad-crested weir with upstream and downstream ramps and horizontal crest (BCW-UDR-HC). It was found that for both the BCW-UDR-NSC and the BCW-UDR-PSC , the C d increases with steeper weir crest slope. This shows that the C d is affected by the slope of the crest such that the negative sloped crest more significantly increases the C d than a positive slope. The average increase in value of the C d for the BCW-UDR-NSC with respect the BCW-UDR-PSC is approximately 8%. [ABSTRACT FROM AUTHOR]

Accurate determination of the discharge coefficient play a very important role in estimating the flow discharge over the weirs. As a result, it is significant to estimate the discharge coefficient correctly. The aim of this study is simulation and estimation the discharge coefficients (C d) over the broad-crested weirs with cross section rectangular and suppressed. Hence, numerical simulation of hydraulic characteristics of these weirs were performed by ANSYS FLUENT software and results were obtained. Then two intelligent models of ANN , GPR and hybrid both of models namely ANN-HHO , GPR-HHO were used to determine the discharge coefficients using the efficient parameters and the results of these models were compared. Assessment of the results were performed using the statistical metrics: coefficient of determination (R 2), root mean square error (RMSE), mean absolute error (MAE), scatter index (SI) and Kling-Gupta efficiency (KGE) and graphical diagrams including violin plot, percent relative error (RE%) plot and probability density function (PDF) plot of residuals. It was found that hybrid artificial neural network and gaussian process regression with Harris Hawks optimization (ANN-HHO and GPR-HHO) could improve ANN and GPR models performance in estimating the C d in broad-crested weirs. Overall, results indicated that a combination of the HHO with the ANN (ANN-HHO) model performs better than GPR-HHO model for the estimation of the C d. • Numerical simulation of broad-crested weirs were performed using CFD. • The two intelligent models of ANN , GPR and hybrid both of models namely ANN-HHO , GPR-HHO were used to determine C d. • The ANN-HHO and GPR-HHO could improve ANN and GPR models performance. • A combination of the HHO with the ANN (ANN-HHO) model performs better than GPR-HHO model. [ABSTRACT FROM AUTHOR]

One type of long-crested weir is oblique weir. Oblique weirs are longer than standard weirs. Therefore, they can pass more discharge capacity than weirs at the given channel width. The main objective of the present study was to investigate the efficacy of several intelligent models including multiple linear regression (MLR), Gaussian process regression (GPR), artificial neural network (ANN) and multiple models driven by ANN (MM-ANN) methods in estimating oblique weir discharge coefficient (C d). Different input combinations were predicted using the variables of H/P , P/L e , and W/L e and the output coefficient of discharge. Prediction models were analyzed by statistical index, including root mean square error (RMSE), correlation coefficient (R), error percentage chart, relative error (RE%) plot, Kling-Gupta efficiency (KGE), probability density function (PDF) plot, scatter plot, scatter plot of error residuals and Taylor's diagram. Obtained results showed that the ANN model performed best by combining the inputs of the three variables (i.e., H/P , P/L e , and W/L e) with R = 0.746 and RMSE = 0.065 among the standalone models. Eventually, the proposed hybrid model MM-ANN was most accurate in estimating the oblique weir C d by improving the prediction results of the implemented models. • Three intelligent models such as MLR, GPR and ANN methods were applied to calculate the nonlinear weir discharge coefficient. • The hybrid multiple model (MM-ANN) was carried out and examined to amend the estimation efficacy of Cd. • Prediction models were analyzed by probability density function plot, scatter plot of error residuals and Taylor's diagram. • Hybrid model MM-ANN was most accurate in estimating the oblique weir C d. [ABSTRACT FROM AUTHOR]

The barriers for the development of continuous monitoring of Suspended Sediment Concentration (SSC) in channels/rivers include costs and technological gaps but this paper shows that a solution is feasible by: (i) using readily available high-resolution images; (ii) transforming the images into image analytics to form a modelling dataset; and (iii) constructing predictive models by learning inherent correlation between observed SSC values and their image analytics. High-resolution images were taken of water containing a series of SSC values using an exploratory flume. Machine learning is processed by dividing the dataset into training and testing sets and the paper uses the following models: Generalized Linear Machine (GLM) and Distributed Random Forest (DRF). Results show that each model is capable of reliable predictions but the errors at higher SSC are not fully explained by modelling alone. Here we offer sufficient evidence for the feasibility of a continuous SSC monitoring capability in channels before the next phase of the study with the goal of producing practice guidelines. [ABSTRACT FROM AUTHOR]