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Due to their superior technical and hydraulic performance and minimal environmental impact, porous weirs have emerged as a feasible alternative to traditional impermeable solid weirs in water transmission and distribution systems. This research study assesses the hydraulic performance of porous broad-crested weirs (PBCWs) with sloping crests. To accomplish this, 30 PBCW models were designed and tested under various operating conditions, including free and submerged flow scenarios. A comparative analysis was conducted to evaluate the performance of PBCWs with and without sloping crests, with the results being compared against a solid broad-crested weir (SBCW) model. The findings revealed that PBCWs with an upstream crest slope exhibited an average increase of 38% in the discharge coefficient compared to similar SBCWs. Similarly, PBCWs with a downstream crest slope demonstrated an average increase of 28% in the discharge coefficient. Additionally, PBCWs with sloping crests showcased heightened sensitivity to changes in tailwater levels compared to PBCWs with horizontal crests, with PBCWs featuring an upstream crest slope being more responsive than those with a downstream crest slope. Finally, leveraging extensive experimental data, empirical equations were derived using nonlinear multi-variable regression and gene-expression programming techniques to accurately represent the free flow discharge coefficient and submerged flow discharge reduction factor. [ABSTRACT FROM AUTHOR]

Abstract Road traffic which results in significant time lags, increased fuel consumption, and financial losses, remains a noteworthy challenge in developed and developing countries. As a result, the Ethiopian Government and the City Administration of Addis Ababa have built extensive road networks and imposed restrictions on driving, vehicle acquisition and parking. However, despite all these efforts, drivers and passengers waste significant time on long traffic queues, resulting in unpredictable and delayed travel. The current study investigated the cost of travel time delay, vehicle operating costs, time reliability, and the factors influencing these variables. The study used questionnaires, measurements, and traffic counting techniques to collect data from nine road segments. The sample comprised 3240 participants. The cost functions of both drivers and passengers were examined using a multiple linear regression model, with estimation performed using ordinary least squares. According to the findings, the economic costs of congestion depend on the number of lanes, the length of the road segment, the volume of traffic, and the respondents’ income level. The study also revealed that travel, vehicle operation, and unreliability costs account for 74%, 6%, and 20%, respectively, of the total congestion costs.

In this paper, the scour downstream of a trapezoidal Piano key weir (PKW) is investigated under free and submerged flow conditions. For this purpose, an experimental model was used in a laboratory channel with a length of 10 m, width of 0.75 m, and height of 0.8 m at various discharges and tailwater depths. The results showed an increase and decrease in the maximum scour depth with an increase in the discharge and submergence ratio, respectively. In addition, increasing the particle Froude number enhanced the geometric features of the scour hole downstream of the PKW. The rate of bed changes slowed down over time. The average values of maximum scour depth, the distance of the maximum scour depth from the weir toe, maximum scour hole length and weir toe scour depth increased in the free flow compared to the submerged flow. The scour hole volume and scour hole area in the submerged flow were less compared to the free flow. The average maximum level of the sedimentary ridge in the free flow is less than the submerged flow. New equations for calculating the geometric characteristics of the scour hole downstream of the trapezoidal PKW are presented with acceptable accuracy.

Road traffic which results in significant time lags, increased fuel consumption, and financial losses, remains a noteworthy challenge in developed and developing countries. As a result, the Ethiopian Government and the City Administration of Addis Ababa have built extensive road networks and imposed restrictions on driving, vehicle acquisition and parking. However, despite all these efforts, drivers and passengers waste significant time on long traffic queues, resulting in unpredictable and delayed travel. The current study investigated the cost of travel time delay, vehicle operating costs, time reliability, and the factors influencing these variables. The study used questionnaires, measurements, and traffic counting techniques to collect data from nine road segments. The sample comprised 3240 participants. The cost functions of both drivers and passengers were examined using a multiple linear regression model, with estimation performed using ordinary least squares. According to the findings, the economic costs of congestion depend on the number of lanes, the length of the road segment, the volume of traffic, and the respondents' income level. The study also revealed that travel, vehicle operation, and unreliability costs account for 74%, 6%, and 20%, respectively, of the total congestion costs. [ABSTRACT FROM AUTHOR]

The attention of researchers and engineers has been attracted to gabion weirs due to their environmental, hydraulic, and stability capabilities compared with solid weirs. One of the possible problems of the weirs is the partial blockage caused by sedimentation upstream of them. This research experiment investigates the hydraulic performance of gabion broad-crested weirs (GBCWs) with an upstream partial blockage. For this purpose, a total of 147 experiments were studied with different conditions for free-flow conditions. The weirs were tested with five partial blockage conditions between 0% and 100% of the weir height (0, 0.25P, 0.5P, 0.75P, and P). The results showed that increasing the partial blockage decreases the discharge coefficient. The changes in the discharge coefficients are minor for partial blockage less than 0.25P, and for partial blockage greater than 0.5P, the discharge coefficients are significantly reduced. As the partial blockage increases, the effect of filling-material size in gabion weirs decreases. Finally, a relationship was developed using the nonlinear regression analysis approach to estimate the discharge coefficient in the GBCWs with partial blockage. HIGHLIGHTS This paper aims to study the effect of partial blockage upstream of a gabion broad-crested weir on its hydraulic performance.; The occurrence of blockage upstream of weirs has changed their hydraulic performance, and this phenomenon should be considered in the design phase, especially in flood-prone waterways.; A review of the research background shows that this phenomenon in gabion weirs has not been evaluated. Therefore, this research has been done to cover this gap.; Empirical relationships were extracted based on the nonlinear regression method to calculate the discharge coefficient of GBCWs with partial blockage.;

Pivot weirs are one of the most important structures for regulating the water level in rivers and canals. These weirs are constructed with one or more gates in a row in the waterways. Changing the angle of each gate is done individually with an independent system. Based on available information, the hydraulic performance of this type of weirs (especially in several gates and different angles) in different operational conditions has not been investigated. In present study, pivot weirs with two gates are simulated using Ansys CFX software with the angles of 27.8 to 90 degree and the discharges between 40 to 130 L/s. Further, the importance of the open space between the two adjacent weirs with different angles (lack of retail wall) and its hydraulic behavior have been studied. The model was calibrated based on valid laboratory data and using the K-ϵ turbulence model. Therefore, the weirs with equal angles were studied in the first step. In this case, the effective discharge angle coefficient was studied and its maximum value compared to the vertical angle was obtained 1.076 for the angle of 52°. Furthermore, relationships for discharge coefficient versus upstream water depth were developed. In the next step, the effective length of the crest was found to be increases by 30% under unequal angles operation and the discharge coefficient raised by 1.3 to 2.4 times. Also, it was recognized that, in case of two weirs with unequal angles, about 26% to 69% of the flow passes through the distance between the two weirs. Therefore, the performance of unequal angles operation seems to be more effective in controlling the water level and discharge in different conditions and especially in flood events.

Pivot weirs are one of the most important structures for regulating the water level in rivers and canals. These weirs are constructed with one or more gates in a row in the waterways. Changing the angle of each gate is done individually with an independent system. Based on available information, the hydraulic performance of this type of weirs (especially in several gates and different angles) in different operational conditions has not been investigated. In present study, pivot weirs with two gates are simulated using Ansys CFX software with the angles of 27.8 to 90 degree and the discharges between 40 to 130 L/s. Further, the importance of the open space between the two adjacent weirs with different angles (lack of retail wall) and its hydraulic behavior have been studied. The model was calibrated based on valid laboratory data and using the K-? turbulence model. Therefore, the weirs with equal angles were studied in the first step. In this case, the effective discharge angle coefficient was studied and its maximum value compared to the vertical angle was obtained 1.076 for the angle of 52°. Furthermore, relationships for discharge coefficient versus upstream water depth were developed. In the next step, the effective length of the crest was found to be increases by 30% under unequal angles operation and the discharge coefficient raised by 1.3 to 2.4 times. Also, it was recognized that, in case of two weirs with unequal angles, about 26% to 69% of the flow passes through the distance between the two weirs. Therefore, the performance of unequal angles operation seems to be more effective in controlling the water level and discharge in different conditions and especially in flood events. [ABSTRACT FROM AUTHOR]

The head-discharge relationship for sharp-crested weirs is developed based on the energy consideration upstream and at the crest of the weir. The discharge for weirs of finite crest length is estimated by correlating the critical depth and total energy at the upstream of the weir. In both cases, discharge is linked with the total head. Therefore, prediction of discharge for both sharp-crested weirs and weirs of finite crest length requires an iterative solution method. The present technical note formulates the relationship between the discharge coefficients based on water and total heads to estimate the error associated with implementation of head-discharge equation based on the head. The proposed prediction curves are used to convert the iterative solution method based on the total head to a direct solution strategy based on the water depth at the upstream of sharp-crested weirs and weirs of finite crest length with either a sharped-edge or rounded entrance. Based on the similarity of velocity profiles in gate flow, it is concluded that a distance as short as 2.4 times of the water head is suitable enough to measure the upstream water depth. In sharp-crested weirs, the effect of velocity head is negligible for the approach velocity ratio smaller than 0.1. Different correction curves were developed for weirs of finite crest length based on the ratio of water head to the crest length of weirs.

A series of numerical simulations was performed to study the discharge capacity of symmetrical hump weirs in free flow condition. A wide range of ramp slopes was selected from 1 V:1 H to 1 V:5 H and the effects of flow discharge and ramp slope on variations of discharge coefficient were investigated. The variations of upstream water head with discharge indicated the existence of two distinct flow regimes on free flow over symmetrical hump weirs. It was found that the discharge coefficient increased with increasing the upstream water head until the maximum discharge coefficient was achieved. Further increase of water head caused a reduction in discharge coefficient and the flow regime became inefficient. The proposed models for prediction of discharge characteristics of sharp-crested weirs with an upstream and (or) downstream ramp(s) from the literature were also compared with the discharge capacity of sharp-crested weirs to study the effects of ramp slope. It was found that the available head–discharge models are acceptable for hump weirs with small ramp length and more accurate prediction models are required for symmetrical hump weirs with larger ramps. The boundary curve to determine the optimum performance in symmetrical hump weirs was introduced, and the head–discharge models for both efficient and inefficient discharge conditions were proposed. [ABSTRACT FROM AUTHOR]

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid–porous interface. These models include a porous-medium model using Darcy's law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems' behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model's predictive capabilities, and make a probabilistic model comparison. [ABSTRACT FROM AUTHOR]

The experimental simulation between the composite hydraulic structure and the found obstacles in the downstream region is a challenging process due to the energy losses and kinematic dissipation. The current work focuses on a comparative analysis of free flow conditions that exist without obstacles and submerged flow conditions that occur due to obstacles. It indicates the evaluation of hydraulic variables and geometrical variables of composite hydraulic structure for both flow conditions. In addition, it includes an investigation of the interaction among these variables. The hydraulic variables include actual discharge, flow velocity, flow cross-sectional area that crosses the gate, downstream water depth, discharge coefficient, Reynolds number and, Froude number, while the vertical distance between the weir and gate represents the geometry variable. The interference between the weir discharge and gate discharge plays a significant role in the result fluctuation and variation for both flow conditions, while the form and size of the obstacles only have a major effect on the submerged flow. For both flow conditions, the water depth is investigated; there would be a drastic increase in water depth by using obstacles in the downstream area as compared with not using the obstacles. This study adopts different obstacles in shape and size, therefore, the variation of maximum and minimum water levels related to the location will occur.

The head-discharge relationship for sharp-crested weirs is developed based on the energy consideration upstream and at the crest of the weir. The discharge for weirs of finite crest length is estimated by correlating the critical depth and total energy at the upstream of the weir. In both cases, discharge is linked with the total head. Therefore, prediction of discharge for both sharp-crested weirs and weirs of finite crest length requires an iterative solution method. The present technical note formulates the relationship between the discharge coefficients based on water and total heads to estimate the error associated with implementation of head-discharge equation based on the head. The proposed prediction curves are used to convert the iterative solution method based on the total head to a direct solution strategy based on the water depth at the upstream of sharp-crested weirs and weirs of finite crest length with either a sharped-edge or rounded entrance. Based on the similarity of velocity profiles in gate flow, it is concluded that a distance as short as 2.4 times of the water head is suitable enough to measure the upstream water depth. In sharp-crested weirs, the effect of velocity head is negligible for the approach velocity ratio smaller than 0.1. Different correction curves were developed for weirs of finite crest length based on the ratio of water head to the crest length of weirs. [ABSTRACT FROM AUTHOR]

Abstract: Predicting the extent of local scouring downstream of hydraulic structures has been one of the topics of interest to researchers in recent years. In this research, downstream scouring of a trapezoidal piano key weir under changes in the hydraulic conditions of the flow and the height of the flow drop passing through the weir in a channel with a length of 10 meters and a width and height of 0.75 and 0.80 meters in the hydraulic laboratory of Water Engineering Group. And hydraulic structures of Tarbiat Modares University of Tehran have been studied. Uniform and non-sticky sediments with an average diameter of 2 mm in length and width of 3 and 0.75 m downstream of the piano key weir were used. All experiments were performed under free flow conditions. The results showed that the maximum occurrence of scour depth with increasing flow drop height is farther away from the weir. The maximum scour depth increases with increasing flow drop height. Scouring in the transverse middle of the bed is less than its walls. Increasing the height of the flow drop is accompanied by more changes in the topography of the bed.

The issues of scouring around a bridge have become prominent in recent research mainly due to recurrent extreme weather events. Thus, designing a bridge with the appropriate protection measures is essential to safeguard it against failure, which may take place due to scouring from high flows resulting from extreme weather events. Bridges may become partially or entirely submerged during extreme weather events such as large floods and are subject to pressure-flow scour, a condition where the flow is directed downward and under the bridge deck, creating an increase in flow velocity and a corresponding increase in bed scour. This study aims to explore the pressure-flow scour depth under a bridge deck without piers in the presence of two vertical wall abutments under clear water experiments. Sixty-six tests were conducted involving the approach flow depth, bed material size, contraction length, contraction width, and bridge opening for both pressure and free surface flow conditions. An empirical equation was deduced to determine the maximum scour depth, which could be applied as a preliminary design for bridges under pressure-flow conditions. The experimental data were used to determine the performance of the earlier models of pressure-flow scour. The results revealed that for pressure-flow conditions, the maximum scour depth increased by a factor between 2.15 and 9.81 times the maximum scour depth under free surface flow conditions. With same flow depth, when the relative bridge length was increased from 5 to 7.5 and 7.5 to 10, the maximum scour depth decreased by up to about 7.4% and 2.3%, respectively. When the relative bridge width was decreased from 5.5 to 5.2 and 5.2 to 4.4, the maximum scour depth increased by up to about 45.6% and 81.2%, respectively. [ABSTRACT FROM AUTHOR]

In the current study, three machine learning (ML) models, i.e. Gaussian process regression (GPR), generalized regression neural network (GRNN), and multigene genetic programming (MGGP), were developed for predicting the discharge coefficient (Cd) of a radial gate under two different flow conditions, i.e. free and submerged. The modeling development of the flow and geometry input variables for the Cd was determined based on statistical correlations. We also performed a sensitivity analysis of the input variables for the Cd. The modeling results indicated that the developed ML models attained acceptable predictable performance; however, the prediction accuracy of the models was better under the free flow condition. In quantitative terms, the minimum root mean square error (RMSE) value was 0.010 using the GPR model and 0.019 using the MGGP model for the submerged and free flow conditions, respectively. The sensitivity analysis evidenced that the ratio of the gate opening height to the depth of water in the upstream (W:Yo) was the influential variable for the Cd under the free flow condition, whereas the ratio of the depth of water in the upstream to the depth of water in downstream (Yo:YT) was the influential variable for the Cd under the submerged flow condition. [ABSTRACT FROM AUTHOR]

Sluice gates are commonly used to measure water discharge and to adjust the water level in open canals. Estimation of head loss (ΔE) and discharge coefficients (Cd) for a sluice gate is essential for the design of open canals. Depending on the downstream water level, free or submerged flow conditions may occur. Although there have been some investigations on Cd for sluice gates, a comprehensive literature review shows that there are no studies of ΔE (to the best knowledge of the authors). Knowledge of ΔE is necessary for the design of intakes and irrigation canal inverts. This study investigates ΔE and Cd using scaled experimentation. Results show that ΔE for free flow is greater than that for submerged flow conditions. Meanwhile, discharge coefficients in a free flow are greater than those under submerged flow conditions. Relative energy losses (ΔE) have a minimum value of 0.271 and a maximum value of 0.604. These high energy losses cannot be ignored in intake structures and canal-designing processes, and their impact on minor canal inverts receiving water from main canals should be considered. Application of multiple nonlinear regression (MNR) models is presented for predicting ΔE and Cd. The MNR method yields accurate predictions. [ABSTRACT FROM AUTHOR]

In order to calculate and predict the discharge flow through and over the gabion weir, 33 experimental broad-crested gabion models were carried out through the sand bed condition. The flow conditions through and over the gabion were presented as three classifications which involved partial flow conditions through a gabion, fully gabion flow through a gabion weir, and overflow on a gabion weir. These classifications were considered due to the free flow conditions. Based on the partial and fully gabion flows, an equation was proposed to calculate the gabion flow. Moreover, the flow discharge over the gabion was considered based on the broad-crested weir formula and then, the coefficient discharge of broad-crested gabion weir was proposed based on experimental measurements. Comparison between the proposed values and experimental measurements illustrates that good agreement is between the proposed and experimental flow discharges. Also, the investigation of flow variations through the gabion showed that the error of gabion equation increased significantly due to overflowing on gabion weir. In order to raise the accuracy of the calculation process of flow discharge through the gabion an equation was proposed based on the geometry and Darcy Wisbech’s parameters. The porosity, length, and particle size were defined based on Darcy Wisbech equations. Some math indexes were considered for this equation and by employing the Mathematical software, these parameters were presented based on the non-liner technique. The error was measured based on the experimental and proposed values and the result of the comparison pointed to the suitable agreement between the two groups of values. Finally, the maximum scour hole was measured by point-gauge along the longitudinal section. Based on threshold velocity and geometrical and hydraulic parameters, an equation was proposed to predict the maximum scour hole depth at the downstream of the broad-crested gabion weir.

In the current study, three machine learning (ML) models, i.e. Gaussian process regression (GPR), generalized regression neural network (GRNN), and multigene genetic programming (MGGP), were developed for predicting the discharge coefficient (Cd) of a radial gate under two different flow conditions, i.e. free and submerged. The modeling development of the flow and geometry input variables for the Cd was determined based on statistical correlations. We also performed a sensitivity analysis of the input variables for the Cd. The modeling results indicated that the developed ML models attained acceptable predictable performance; however, the prediction accuracy of the models was better under the free flow condition. In quantitative terms, the minimum root mean square error (RMSE) value was 0.010 using the GPR model and 0.019 using the MGGP model for the submerged and free flow conditions, respectively. The sensitivity analysis evidenced that the ratio of the gate opening height to the depth of water in the upstream (W:Yo) was the influential variable for the Cd under the free flow condition, whereas the ratio of the depth of water in the upstream to the depth of water in downstream (Yo:YT) was the influential variable for the Cd under the submerged flow condition.

Abstract Background Local scour is one of the main problems affecting the stability and operation of control hydraulic structures. Many techniques were used to control the resulting scour. In the recent study, a new technique was used to control local scour downstream single-gate hydraulic regulator by using side flow jets. This study aimed to demonstrate the effect of side jets at different angles on the local scour parameters (depth, length, and volume) and energy dissipation in the downstream hydraulic regulator. Results A physical model was used to represent the open channel, regulator, and the side jets with different angles. Five flow discharges, four jet angles, and three gate openings were applied through the experiment. The experiment results showed that the presence of side jets had a remarkable effect on the parameters of the local scour hole and energy dissipation. They dissipated more energy of hydraulic jump than in the absence of jets, and consequently, scour hole dimensions were significantly reduced. Regression analysis was used to deduce equations that can predict the development of local scour downstream sluice gate considering the inclination angle of side flow jets under different flow conditions. Conclusions Side flow jets can be used as scour reducer techniques with the advantages of eliminating the jet clog produced from sediments and suspended solids.

The experimental simulation between the composite hydraulic structure and the found obstacles in the downstream region is a challenging process due to the energy losses and kinematic dissipation. The current work focuses on a comparative analysis of free flow conditions that exist without obstacles and submerged flow conditions that occur due to obstacles. It indicates the evaluation of hydraulic variables and geometrical variables of composite hydraulic structure for both flow conditions. In addition, it includes an investigation of the interaction among these variables. The hydraulic variables include actual discharge, flow velocity, flow cross-sectional area that crosses the gate, downstream water depth, discharge coefficient, Reynolds number and, Froude number, while the vertical distance between the weir and gate represents the geometry variable. The interference between the weir discharge and gate discharge plays a significant role in the result fluctuation and variation for both flow conditions, while the form and size of the obstacles only have a major effect on the submerged flow. For both flow conditions, the water depth is investigated; there would be a drastic increase in water depth by using obstacles in the downstream area as compared with not using the obstacles. This study adopts different obstacles in shape and size, therefore, the variation of maximum and minimum water levels related to the location will occur. [ABSTRACT FROM AUTHOR]

The present study investigate 12 experimental broad-crested gabion models. In order to investigate the flow regimes over this structure, hydraulic characteristics were measured under different submergence conditions. A comparison of coefficient discharge values showed that a significant increase in these values was observed between the broad-crested and broad-crested gabion weirs. It seemed that the passed flows through gabion weir could raise the discharge coefficient values versus the same values with same hydraulic condition for solid broad-crested weir. To predict the discharge values over this weir, reduction factor has been calculated for the experiments in different submerged ratio. By considering the submergence ratio, an equation has been proposed to calculate these values. Three regimes have been introduced to measure the water surface profiles as free flow, (I) surface jump regime, (II) surface wave regime, (III) Deeply submerge regime. Due to increase the tail water height, water surface profile was measured as proposed regimes. The surface jump regime was defined as a downstream hydraulic jump which was developed from downstream location of channel to the weir crest. Additionally, the water surface turn to the series of downward waves which is called surface wave regime. By increasing the submerged ratio, the surface wave regime was vanished as the deeply submerged condition. The submerged ratio 0.18 has been proposed to region the surface jump regime and surface wave regime. Also, based on submerged ratio, an equation has been proposed to separate the surface wave regime and deeply submerge regime. The longitudinal velocity has been measured by ADV probe at the downstream broad-crested weir over the longitudinal section. Comparing between measured longitudinal velocity and color injection illustrates that increasing the submergence ratio causes the flow within gabion weir has marginally decreased and this flow is dependent on submergence ratio. The color injection results show the passed the performance of gabion weir in deeply submerged regime is same as broad-crested weir and the flow with in gabion will be negligible over the developed deeply submerged regime.

A comprehensive analysis on the hydraulics of flow over Triangular Weirs of Finite Crest Length (TWFCL) with both a sharp and a round upstream entrance was performed in free flow, modular limit, and submerged flow conditions. Many researchers studied the hydraulics of flow over TWFCLs and proposed empirical formulations that require iterative methods or need some parameters such as boundary layer thickness and Froude number which are difficult to estimate in the field. This study used the available data in the literature and proposed direct correlations between the apex angle, θ , and discharge coefficient, C d , using a multi-regression analysis. The proposed non-linear formulation for prediction of discharge coefficient has an average variation of 3 % with experimental data for TWFCL with a round upstream edge and it is applicable for 30o ≤ θ ≤ 90o. A linear model was proposed for prediction of discharge coefficient in TWFCL with larger apex angles with an average variation of less than 2 %. The variation of modular limit with normalized water head indicated that TWFCLs are more resistant to the downstream water level raise than that of classic weirs of finite crest length. The effects of weir's geometry on variations of discharge reduction factor with the submergence ratio was found to be negligible in TWFCLs. A non-linear model was proposed to predict discharge reduction factor of TWFCL which was independent of weir's geometry and θ. • A non-linear equation was introduced to predict discharge coefficient of TWFCL. • For a constant head, C d increases with increasing apex angle for 140 ≤ θ ≤ 160. • The TWFCLs are more resistant in downstream water level than that of classic weirs. • A formula was proposed to predict the submerged discharge of TWFCL. [ABSTRACT FROM AUTHOR]

Gates are commonly used to adjust water flow in open channels. By using an oblique/inclined gate, the water transferring capacity of open irrigation canals can be increased. Investigation of free and submerged discharge coefficients for inclined sluice gates is the focus of the present study. First an experimental apparatus incorporating an inclined gate was created. The inclined angle (β) and gate opening (a) were experiment variables, and the five inclination angles include: 0° (vertical gate), 15°, 30°, 45° and 60°. Experimental results showed a greater convergence of flow lines under the gate and increasing the gate angle causes the discharge coefficient to increase. Also experiments showed that increasing the submergence rate (yt/a), decreases the inclined gate discharge coefficient. Performance metrics were created for the experimental results. The metrics utilized Gaussian process (GP) regression, support vector machine (SVM), artificial neural networks (ANN), generalized regression neural network (GRNN), random forest (RF) regression and random tree (RT) based models which were used to predict discharge coefficients (Cd) in both submerged and free flow conditions. The model input parameters were the ratio of the upstream water depth to gate opening (y/a) and the inclined angle (β) for free flow and also the submergence rate (yt/a) for submerged flow. The prediction models show that the ANN model in free flow conditions has the following performance metrics: Coefficient of determination, R2 = 0.9957, Root Mean Square Error (RMSE) = 0.0044, and Mean Absolute Error (MAE) = 0.0017. The performance metrics for submerged flow conditions were R2 = 0.9922, RMSE = 0.0079 and MAE = 0.0054. The ANN approach is the most accurate model compared to the others.

This paper aims to conduct a series of laboratory experiments in case of steady-state flow for the new size 7 ̋ throat width (not presented before) of the cutthroat flume. For this size, five different lengths were adopted 0.535, 0.46, 0.40, 0.325 and 0.27m these lengths were adopted based on the limitations of the available flume. The experimental program has been followed to investigate the hydraulic characteristic and introducing the calibrated formula for free flow application within the discharge ranged between 0.006 and 0.025 m3/s. The calibration result showed that, under suitable operation conditions, the suggested empirical formulas can accurately predict the values of discharge within an error ± 3%.

The water flow under a high-dam gate with a small opening has rarely been studied. The discharge coefficient and head loss under sluice gates are studied experimentally, with the relative gate opening less than 0.10, including the free and submerged flow. The semiempirical formula for the discharge coefficient is proposed, which is used to estimate the overflow capacity of the free and submerged flows with a relatively small gate opening. The equation of the bed friction head loss of the submerged flow in the boundary layer is derived by using boundary-layer theory. The local head loss and the head loss caused by the flow turbulence in the eddy area are estimated, respectively. The results show that for the free flow, the inflection point of the vertical contraction coefficient, discharge coefficient, and total-head-loss coefficient varying with the relative gate opening was 0.04. The head loss caused by the flow turbulence in the eddy area played a leading role in the total head loss for submerged flow. The results can provide a reference for the design and operation of high-dam deep-hole gates. [ABSTRACT FROM AUTHOR]

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The issues of scouring around a bridge have become prominent in recent research mainly due to recurrent extreme weather events. Thus, designing a bridge with the appropriate protection measures is essential to safeguard it against failure, which may take place due to scouring from high flows resulting from extreme weather events. Bridges may become partially or entirely submerged during extreme weather events such as large floods and are subject to pressure-flow scour, a condition where the flow is directed downward and under the bridge deck, creating an increase in flow velocity and a corresponding increase in bed scour. This study aims to explore the pressure-flow scour depth under a bridge deck without piers in the presence of two vertical wall abutments under clear water experiments. Sixty-six tests were conducted involving the approach flow depth, bed material size, contraction length, contraction width, and bridge opening for both pressure and free surface flow conditions. An empirical equation was deduced to determine the maximum scour depth, which could be applied as a preliminary design for bridges under pressure-flow conditions. The experimental data were used to determine the performance of the earlier models of pressure-flow scour. The results revealed that for pressure-flow conditions, the maximum scour depth increased by a factor between 2.15 and 9.81 times the maximum scour depth under free surface flow conditions. With same flow depth, when the relative bridge length was increased from 5 to 7.5 and 7.5 to 10, the maximum scour depth decreased by up to about 7.4% and 2.3%, respectively. When the relative bridge width was decreased from 5.5 to 5.2 and 5.2 to 4.4, the maximum scour depth increased by up to about 45.6% and 81.2%, respectively.

Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence. • Simulation results of Hump weirs indicated ±10 % error on prediction of water surface level. • Numerical outputs indicated ±5 % error in prediction of discharge coefficient in Hump weirs. • A direct correlation was found between ramp slope and the magnitude of modular limit. • Modular limit increased with increasing ramp slope and discharge. • Energy losses in submerged Hump weirs decreased linearly with submergence. [ABSTRACT FROM AUTHOR]

In this paper, we propose and numerically solve a model considering confined flow in fractured porous media coupled with free flow in conduits. Such a situation arises, for example, for fluid flows in fractured vuggy carbonate reservoirs and caves/conduits, where a matrix and fractures are the main spaces for fluid storage and flow. The flow in caves and conduits is governed by the Stokes equation; the flow in fractured porous media, which consists of both a matrix and fractures, is described by a coupled Darcy–Darcy (bulk–fracture) model. Then, the two models are coupled through suitable (physically consistent) interface conditions on the interface between fractured porous media and caves/conduits, playing a key role in a physically faithful simulation that achieves high accuracy. The construction of all the interface conditions of the coupled model is based on the fundamental properties of the traditional bulk–fracture model and the well-known Stokes–Darcy model. The weak formulation is derived for the proposed model, and the well-posedness of the model is theoretically analyzed. We also propose a polyhedral discontinuous Galerkin finite element approximation for the Stokes flow in conduits and Darcy flow in the porous matrix, which is coupled with a conforming finite element scheme for the flow in the fracture. Optimal error estimates in a suitable energy norm are obtained. Two-dimensional numerical experiments are conducted to validate the proposed model and to demonstrate the features of both the model and the numerical method, such as the optimal convergence rate of the numerical solution; the detail flow characteristics around fractures, the matrix, and conduits; and the applicability to real-world problems. [ABSTRACT FROM AUTHOR]

• The CTM assumes free-flow speeds (ffs's) are exactly one cell per time step (1 cpts). • but in reality, ffs's vary over time and space – hence often less than 1 cpts. • Allowing ffs's less than 1 cpts, makes CTM solutions very inaccurate. • Proposed remedy: for cells with ffs less than 1 cpts, use actual ffs, not the CTM. • Problem and remedy (CTM and 'revised' CTM) are illustrated for simple examples. In the cell transmission model (CTM), time is discretised into time-steps and links discretised into cells. In the original CTM, and usually thereafter, the cell lengths are chosen so that, at free-flow speeds (ffs), traffic travels exactly one cell per time-step (1 cpts), so that the ffs, denoted α, is exactly α = 1 cpts and, to avoid computational complications, the length of each cell is normally held constant over time. But the actual observed ffs's in a cell will often differ by time of day or traffic type or traffic lane, or due to speed limits that vary over time or space, or due to stochastic effects. By construction, the maximum ffs in each cell is 1 cpts (α = 1), hence when the ffs is varying within a cell, it will often be less than 1 (α < 1). We show that when traffic in a cell has a ffs α < 1 cpts then the flows and occupancies obtained from the standard CTM can be very inaccurate. For example, consider a cell of length 1 that is in a free flow state with free-flow speed α < 1 and no further flow into the cell. Then all traffic in the cell will have exited by time 1/α and the cell will then be empty. In contrast, for the same scenario, the CTM lets a fraction α < 1 of the remaining traffic in the cell exit in each time step, so that the cell outflow and occupancy decline geometrically toward zero, so that the cell never fully empties. The problem is serious since in traffic networks there may be large numbers, or a large proportion, or a majority, of cells and links that are in a free-flow state for all or part of the time span being modelled. To overcome the above problem, we propose that the CTM not be applied to cells that are in a free-flow state with ffs α < 1 cpts. Instead, for those cells and links, we let traffic move forward at its ffs rather than as computed from the CTM. This is easily accomplished since, in the CTM the computations roll forward one time step at a time and, in each time step, the cell occupancy is updated from the previous time step, hence is known and the known occupancy immediately indicates whether the cell will be in a free-flow state. [ABSTRACT FROM AUTHOR]

Boundary conditions at the interface between the free-flow region and the adjacent porous medium is a key issue for physically consistent modeling and accurate numerical simulation of flow and transport processes in coupled systems due to the interface driven nature of such processes. Interface conditions available in the literature have several weak points: most of them are suitable only for flows parallel to the fluid-porous interface, some are restricted to specific boundary value problems, and others contain unknown model parameters which still need to be determined. These facts severely restrict the variety of applications that can be successfully modeled. We propose new interface conditions which are valid for arbitrary flow directions. These coupling conditions are rigorously derived using the theory of homogenization and boundary layers. All effective parameters appearing in these conditions are computed numerically based on the geometrical configuration of the coupled system. The developed conditions are validated by the comparison of numerical simulation results for the coupled Stokes--Darcy model and the pore-scale resolved model. In addition, the new interface conditions are compared with the classical conditions to demonstrate the advantage of the proposed conditions. [ABSTRACT FROM AUTHOR]

We couple a dynamic, fully implicit non‐isothermal two‐phase, two‐component pore‐network model (PNM) to a free‐flow domain where the single‐phase flow Navier‐Stokes equations with component and energy transport are solved. A monolithic coupling scheme guarantees the conservation of mass, momentum and energy across the coupling interface and allows solving the system without any coupling iterations. We present a numerical example and show that the model is able to temporally resolve the pore‐local flow and transport dynamics of an evaporation process. Key Points: We present a coupled free‐flow/pore‐network model for simulating the pore‐scale dynamics of evaporation processesThe dynamic, fully implicit pore‐network model considers phase change and energy transportThe monolithic coupling scheme is inherently mass, energy and momentum conservative and does not require any coupling iterations [ABSTRACT FROM AUTHOR]

In many applications, the adjustment of a gate opening to a specific value is crucial for the passage of a defined outflow or to maintain an upstream water level that serves upstream turnouts. Previous work used trial-and-error and interpolation methods to calculate the opening of sluice gates. This study concentrates on the development of a way to estimate the opening of sluice and radial gates to achieve the desired discharge or upstream water level. In addition to energy and momentum (E-M) principles, this paper develops relationships to determine the openings of sluice and radial gates under free- and submerged-flow conditions. Based on experimental data, the mean absolute relative errors for calculating the opening of sluice and radial gates under different flow conditions using the previously proposed methods, as well as dimensional analysis, were 4.3% and 7.1%, respectively. In this study, the calculated relative errors in employing E-M principles were reduced from 3.6% to 2.9%, in which the effects of energy loss were overlooked, and the gate's energy coefficient was introduced. [ABSTRACT FROM AUTHOR]