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Quantitative performance indicators of irrigation water management are required the measurement of flow rates at key locations in a conveyance and distribution system. Radial gates have been widely used for the agricultural water management in the irrigation areas, due to the small lifting forces and significant economic benefits. However, the inaccurate calibration is often found in the submerged flow, where the error is as high as 50%. Therefore, it is of great significance for the accurate determination of discharge capacity. This study aims to achieve the accurate water measurement and determination of discharge coefficient in the irrigation areas. The discharge capacity of submerged flow pattern was predicted using support vector machine (SVM), generalized regression neural network (GRNN), extreme learning machine (ELM), and kernel extreme learning machine (KELM). The performance of the models was comprehensively evaluated by evaluation indexes, objective function (OBJ) criteria and uncertainty analysis. At the same time, the Sobol's method was used to quantify the dimensionless parameters using the performance of the optimal model. A systematic evaluation was implemented to obtain the importance of each parameter (the discharge coefficient (Cd)) and the interaction of the parameters. In addition, there was the great variation between important parameters and Cd, according to the discharge characteristics of radial gate. The model evaluation results show that the better performance was found in the KELM with the determination coefficient R²=0.972, the mean absolute percentage error KMAPE=5.038%, the root mean square error KRMSE=0.020, the Willmott’s agreement index KWIA=0.993, and objective function KOBJ=0.0127. The uncertainty analysis show that the average error of KELM was the lowest (Se=0.00015), the width of confidence band was the narrowest (BD=0.04942), and the range of 95% confidence interval was the smallest (-0.04927~0.04956), indicating the highly consistent data and the high reliability of the sample. Therefore, the KELM shared the higher accuracy and robustness, compared with the SVM, GRNN, and ELM models. An efficient and high-precision model was achieved for the flow calibration of the radial gate. The Sobol’s sensitivity analysis showed that the main influencing factors were the ratio of trunnion pin height to upstream water depth (h/Y0), the ratio of gate radius to upstream water depth (R/Y0), and the ratio of gate width to upstream water depth (B/Y0). Furthermore, these parameters (h/Y0, R/Y0, B/Y0) should be considered emphatically in the design of radial gates in practice. The first-order sensitivity coefficient and global sensitivity coefficient to Cd were ranked in the descending order of 0.1162, 0.0754, 0.0752, and 0.5311, 0.4966, 0.4959, respectively. Therefore, the global sensitivity coefficient was much higher than the first-order sensitivity, indicating that the interaction of parameters increased the influence of each parameter on the discharge coefficient. The variation between important parameters and discharge coefficient Cd showed that the Cd increased linearly with the increase of h/Y0, R/Y0 and B/Y0. In addition, the smaller the gate opening W was, the larger the increase of the discharge coefficient Cd was. This finding can further improve and enrich the hydraulic mechanism of the radial gate under submerged flow conditions. A strong reference can be offered for the calibration of submerged radial gates during the engineering design in irrigation areas. [ABSTRACT FROM AUTHOR]

Laboratory experiments were conducted out to investigate the regimes of submerged flows over the sharp-crested weirs in sand bed Channel. These kinds of flows were classified as five states such as (I) impinging jet, (II) bed surface flow, (III) surface jump, (IV) surface wave, and (V) surface jet based on the depicted vector plots of the regimes. By increasing the submergence ratio, the impinging jet was developed as a downward jet which was impinged from the weir crest to the downstream. By continue the increasing, flow regime was developed as a bed-surface flow which is supposed that the impinging jet is turned as flow near the bed position instead of having a direct impact with the bed. Additionally, increasing constancy of the submergence ratio causes that the bed-surface regime turned to the surface jump which is accompanied by a hydraulic jump at the water surface. Subcritical condition at downstream of the weir which is provided by raising the tailwater due to constant flow discharge causes that the surface wave regime has vanished at the water surface of the downstream of the weir and some oscillating waves were transferred to downstream. Finally, by considering the maximum range of submergence ratio, the flow regime was changed to the surface jet which was accompanied by a big clockwise vortex at the lower water elevation. The present study classifies these flow regimes based on the velocity components (u, v, w). This approach was chosen by the authors to show the different classification between visual inspection and investigating the velocity direction by ADV. Then, an empirical equation was proposed to show the boundaries of the presented regimes. Also, a dynamic restriction was proposed based on experimental and literate data as a non-eroded status that is due to a submerge ratio, the scour hole is not provided at downstream of sharp-crested weir. [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. [ABSTRACT FROM AUTHOR]

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]

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]

The piano key weir (PK-Weir) is a hydraulic structure used in the irrigation system by its construction on artificial or natural channels such as rivers or irrigation canals, it may be in the submerged state due to an increase in flow or an obstacle downstream of the PK-Weir. Therefore, this type of weir has been the subject of several experimental studies in order to understand the phenomenon of streaming flow on the weir, which led to the development of empirical relationships describing the effects of streaming flow on hydraulic performance. Experimental studies are essential for the design of weirs, but they require a lot of time to collect a real database. The main objective of this paper is to predict the relative head of PK-Weir for submerged flow using artificial neural networks. To do this, we have used the results of our experimental study to develop a neural model. The results obtained were very satisfactory with very acceptable errors (RMSE = 0.0133 and MAE = 0.0066). In addition, a comparative study was made between empirical relationships and the developed model. The results of this comparative study showed a good agreement. [ABSTRACT FROM AUTHOR]

Accurate prediction of the discharge through radial gates is difficult. Existing calibration methods typically provide sufficient accuracy for free flows and submerged flows with jet Froude number at vena contracta larger than 1.7. However, their predictions are poor for submerged flows with jet Froude number less than 1.7. Based on the analysis of experimental data collected by the US Bureau of Reclamation, an empirical indicator was proposed to predict the approximate range of jet Froude number for submerged flows. Accordingly, submerged flows were subdivided into partially submerged flows with fully developed hydraulic jump, and totally submerged flows with undular or no jump. A new discharge calibration method, referred to as the identification method, was developed for the three distinct flow conditions. Verification of the proposed method indicated the discharge prediction accuracies were significantly improved for totally submerged flows. [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]

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]

The hydraulic performance of triangular labyrinth weirs with an upstream pool was experimentally studied in both free and submerged flow conditions. The discharge coefficients based on channel width B and the weir length L were calculated from experimental data. It was found that the additional length provided by the pool can significantly increase the capacity of the new weir design. The tested weir models were found efficient and required less concrete in comparison with classical labyrinth weirs for a relatively low head water to weir height ratio of ho/P=0.17. Empirical formulations were developed to predict the discharge coefficient and the critical depth of flow for labyrinth weirs with an upstream pool. The discharge reduction factor ψ of the new weir design was found to be slightly lower than the ψ value of sharp-crested weirs. Performance of the tested weir models in submerged flow condition was directly compared with the sharp-crested weirs. It was found that the submerged flow discharges of the tested weir models were significantly higher than the corresponding submerged flow discharge in sharp-crested weirs. A power law model was proposed to predict the submerged flow discharge from a given water head. The superior performance of labyrinth weirs with an upstream pool over classical labyrinth and sharp-crested weirs in both free and submerged flow conditions make them a suitable choice as a flow measuring device, depth regulator, and flood control structure. [ABSTRACT FROM AUTHOR]

Acknowledged as a significant cause of bridge failure is abutment scour around bridge foundations. Because of the complexity of flow structures and scour mechanisms around an abutment, abutment scour remains the focus of extensive research. In this study, to elucidate the complex flow physics and resulting sediment transport around an abutment, time development of abutment scour in three flow types of free, submerged orifice, and overtopping were examined by conducting laboratory experiments in a compound channel. Different lengths of erodible abutment were used to explore the effect of flow contraction on the abutment scour. Detailed bed contours at selected time intervals, as well as velocities, for the initial conditions were measured with acoustic Doppler velocimeters during each experiment. From observations, the scouring process and the resulting scour hole shape and scour depth around an abutment over time were found to be inconsistent depending on the flow type and degree of flow contraction. Tracking the maximum scour location over time explained the complex scouring process around an abutment, which is a simultaneous effect of local turbulence and flow contraction. [ABSTRACT FROM AUTHOR]

Abstract The classical sharp-crested weirs are not suitable to implement in irrigation canals with high suspended sediment flow. Over the time, sediment deposition occurs in the upstream of sharp-crested weirs and causes a time variant water level raise in the upstream and consequently variable discharge coefficients. A series of laboratory experiments was carried out to test the hypothesis of strong turbulent formation and three-dimensional flow in the upstream of half-cosine sharp-crested weirs to prevent sediment deposition. To verify this hypothesis, a series of laboratory experiment was carried out for different weir heights and top widths in free and submerged flow conditions. Mean flow structure and turbulent characteristics of half-cosine and rectangular sharp-crested weirs were measured using a micro-Acoustic Doppler Velocimeter (ADV) probe. It was found that the streamwise velocities of half-cosine weirs were higher than the corresponding rectangular weirs, however, the velocity fluctuations in this direction were similar for both types of weirs. Velocity fluctuations in vertical and transverse directions were found to be significant in half-cosine weirs. The results showed higher turbulent kinetic energy below the crest level for half-cosine weirs which made them capable of sediment resuspension and sediment removal. In was found that the introduced weir model are suitable structures for passage of small floating debris and sediments. A head-discharge formulation was also developed based on the geometry of half-cosine weir in free flow and a constant discharge coefficient was obtained by solving the Fresnel integrals. For practical purposes, semi-empirical formulations were also developed to estimate flow discharge in both free and submerged flow conditions. Highlights • Hydraulics of flow over half-cosine sharp-crested weirs was studied. • Coefficient of discharge was estimated using data correlation and solving Fresnel integral. • Transverse velocity fluctuation became a significant contributor of turbulent kinetic energy for half-cosine weirs. • The location of the peak transverse velocity for half-cosine weirs is different from rectangular weirs. • The average turbulent intensity for half-cosine sharp-crested weir is 19.2% higher than that of rectangular weir. [ABSTRACT FROM AUTHOR]

Scour downstream of hydraulic structures is an important problem in engineering. There are many experimental studies on the scour problem, and some empirical relationships were presented in the literature. The biggest challenges in the scour analyses are the requirement of a lot of time and complex hydrodynamics of the liquidsolid interaction. In this study the scour at downstream of submerged sluice flow after an apron was investigated by using 2D computational fluid dynamics (CFD). Some experimental data and relationships in the literature were used to calibrate the numerical analyses. It is observed that the variation of maximum scour versus time is exponential and dimensionless scour profiles fit to third degree curve. The relative percent error is approximately 5-10% between experimental and numerical results. [ABSTRACT FROM AUTHOR]

Extensive experimental investigation has been performed to analyse the behaviour of piano key weir under submerged flow conditions. More than 2500 runs were performed on 14 physical models in an experimental rectangular flume, 15 m long and 0.3 m by 0.45 m cross-section. Effect of submergence phenomenon on the discharge capacity was studied for different discharge values. It was found that the discharge reduction factor Cs is mainly influenced by the submergence factor S. This effect starts when S is greater than the modular submergence limit which proved to be around 0.4 to 0.6. Models with different geometrical parameters were compared to each other and final conclusions about their effect on discharge capacity were achieved. However, the influence of all the geometrical parameters was small (less than 12%). [ABSTRACT FROM AUTHOR]

Accurate estimation of discharge capacity and local hydrodynamics are essential when designing hydraulic structures. Instead of the application of conventionally used empirical relationships, this study introduces a 3D numerical modeling technique which is capable to adequately predict both the discharge-upstream water level relationship and the flow field around weirs. The numerical model, REEF3D, is validated for different hydrodynamic conditions (free-flow and submerged flow) against laboratory data performed for an ogee type weir. Simulated water surface elevations compared with experimental data together with the modeled flow field around the weir suggest that even the complex modular, transition and nonmodular submerged cases can be reproduced by the numerical tool. The study proves that the herein applied numerical solver can be a good alternative of laboratory models for flow analysis at complex hydrodynamic conditions, especially where spatially strongly varying free surface characterizes the flow. [ABSTRACT FROM AUTHOR]

The flow through a triangular plan labyrinth weir is studied for both free and submerged flow conditions experimentally and theoretically. The free flow condition is studied using a new experimental data set collected in this study. For the submerged flow condition, the threshold between free and submerged flow regimes is studied experimentally. Then Buckingham analysis is employed to determine the submerged head-discharge formula of the triangular plan labyrinth weir. Finally, a step by step calibration method is proposed to find the unified discharge coefficient. The proposed discharge coefficient can be used for both free and submerged flow conditions continuously and within the transition zone. [ABSTRACT FROM AUTHOR]

Sluice gates have been widely used and intensively studied, however their submerged flow conditions still call for in depth attention. A large scale experimental setup equipped with Acoustic Doppler Velocimetry, ADV, and electromagnetic flow-meter was used to thoroughly investigate various aspects of the hydraulics of submerged sluice gate. In this study, new experimental data sets are provided, that help better understand and quantify the flow features for submerged sluice gates. According to the experimental data generic fitting are provided for the velocity profiles from which the velocity correction factors can be obtained. Then, the experimentally obtained submerged head loss coefficient is presented and discussed. The results of this study showed that current classical Energy-Momentum methods (EM) failed to accurately determine the flow rate for the cases of highly submergences, while employing the interaction of the energy correction factors and head loss values in the EM model would result in more accurate head-discharge estimation. The new data set provided in this work can be used effectively for the validation of numerical modeling of submerged sluice gates. [ABSTRACT FROM AUTHOR]

Computational Fluid Dynamics (CFDs) analyze software package programs recently gained a high importance in hydraulic engineering. The present study investigates how different sills will affect in terms of flow dynamics. In the study, velocity contours and velocity magnitudes for each sill shapes are investigated. The velocity magnitudes are compared by taking 4 cross-sections from the downstream region. Results showed that sills located at downstream of the channel decrease the velocity magnitude at per selected location. Thereby it was concluded that the sill usages could protect the channel bottom from the cavitational and scouring damages due to high flow velocities. In this respect the study will help to the hydraulic designs in this scope. [ABSTRACT FROM AUTHOR]

Seven hundred ninety-seven field-measured data points were collected to calibrate multiple parallel radial gates. Data were collected from three control structures (i.e., Al-Tawfiki, Al-Menoufi, and Abasi regulators), which are located in the Delta irrigation district of Egypt. Upstream and downstream water depths, gate opening size, and flow discharge was measured at each structure. Additionally, previous calibration methods were reviewed and evaluated. Dimensional analysis with application of the incomplete self-similarity concept demonstrated the best results for the study area. Based on the field measurement data, a simple formula that implicitly considers the discharge coefficient is proposed for estimating the flow rate through submerged parallel radial gates. [ABSTRACT FROM AUTHOR]

Laboratory experiments were carried out to investigate the water surface characteristics of submerged flow over sharp-crested weirs. Interesting observations were made on the water surface profiles near the weir as weir submergence sets in as well as for various stages of submergence. Submerged flow was divided into four regimes: (I) impinging jet, (II) surface jump, (III) surface wave, and (IV) surface jet. It was found that a surface jump turned into a surface wave when the wave trough became level with the tip of the weir. The surface jet regime began as the surface waves faded out. A condition was set to quantify the boundary between the surface wave and surface jet regimes. Based on flow observations, the surface jet regime sets in as the amplitude of the surface wave becomes small (i.e., less than 0.1h, where h is the head). An empirical equation was developed based on the literature data to predict the discharge reduction factor in the generally used discharge equation. This formulation was compared with other formulations in the literature. It was found that the proposed formulation provides a slightly better estimation of flow discharge. [ABSTRACT FROM AUTHOR]

Peak discharges during large floods can often result in submerged orifice flow (also called "pressure flow"), or embankment and bridge overtopping flow, in which the embankment and abutment foundation of a bridge are subjected to severe scour and possible failure. In this study, abutment scour experiments were carried out in a wide, laboratory compound channel to investigate the characteristics of abutment scour for the three flow types of free, submerged orifice, and weir (overtopping) for an erodible but riprap-protected embankment and abutment. Detailed bed contours and three-dimensional (3D) velocities and turbulence quantities were measured with acoustic Doppler velocimeters. The results show that the contracted flow around an abutment (due to lateral or vertical flow contraction) and the local turbulent structures near the downstream face of the bridge are the main features of the flow field responsible for the maximum scour depth near the abutment. Experimental results for combined abutment and contraction scour depth are presented in terms of the theoretical long contraction scour for all three types of flow. The experimental results for maximum scour depth are compared with those of other investigators, and it is shown that the erosional strength of the embankment defines an upper and lower bound for maximum scour depth for a solid abutment versus a riprap-protected embankment and abutment. [ABSTRACT FROM AUTHOR]

In this paper the flow through parallel sluice gates under low flow conditions and with some of the gates closed resulting in symmetrical or asymmetrical gate installations was studied experimentally. The current stage–discharge formula for single sluice gates cannot be used for either free flowing or submerged parallel sluice gates. Then, on the basis of experimental observations, the effect of the closed gates was considered to develop a submergence distinguishing condition curve formula. For both free and submerged regimes, the Π -theorem along with the incomplete self-similarity concept was used to develop head–discharge formulas for symmetrical and asymmetrical gate installations. The proposed formulas were then calibrated using the compiled experimental data. The new approach is shown to be applicable within the entire range of operation, i.e. from free to submerged flow regimes as well as the transition zone. [ABSTRACT FROM AUTHOR]

The flow in a submerged hydraulic jump with three-dimensional (3D) baffle blocks was experimentally studied. An incoming jet with varying supercritical Froude numbers was deflected with one or two rows of 3D baffle blocks for different downstream water depths. Depending on the submergence factor, two flow regimes were observed for which the time-averaged 3D velocity field was measured with an acoustic Doppler velocimeter (ADV). Measurements were conducted at different stations located both upstream and downstream of the blocks and above the crest of the blocks. Velocity measurements were made in a plane located at the center of the middle block (i.e., the centerplane of the flume) and, also, in a plane located at the midpoint between the blocks (off-centerplane). The mean flow pattern was found to be significantly different for the two flow regimes. In the deflected surface jet (DSJ) regime, which occurred at low submergence factors, the major flow features were a small surface roller upstream of the blocks and a larger recirculating flow region located downstream of the blocks. The reattaching wall jet (RWJ) regime, which was formed at large submergence factors, could be characterized by a large surface roller and a small standing eddy just behind the blocks in the centerplane. In both flow regimes, the maximum longitudinal velocity component was observed to decrease rapidly at the blocks and the jet half-width was found to increase quickly. The DSJ regime was found to have a smaller streamwise dimension and to be more effective in reducing the streamwise velocity and increasing the jet half-width. These features can be considered an advantage of the DSJ regime over the RWJ regime; that is, hydraulic structures should be designed such that the DSJ regime occurs over the entire range of tailwater depths that are likely to occur. [ABSTRACT FROM AUTHOR]

A Parshall flume is a common device for measuring open-channel flows. Some Parshall flumes, however, have been modified or constructed without a downstream diverging section. A Parshall flume that does not have its divergent section is known as a Montana flume. Both physical modeling and computational fluid dynamics (CFD), or numerical modeling, have been utilized to assess the accuracy of and calibrate Montana flumes. Montana flumes under free-flow conditions operate similarly to Parshall flumes and, therefore, share the same rating curves. However, Montana flumes that operate under submerged conditions can deviate by as much as 15% from equations used to correct the submerged Parshall flume flow rate. The research summarized in this paper illustrates comparable results between numerical and physical modeling tests performed on a 6-in. (15.2-cm) submerged Montana flume. In addition, with the numerical model calibrated to the physical model, the same numerical procedure is used to expand testing to other sized Montana flumes under submergence. Accordingly, nine sizes of Montana flumes are numerically simulated between 6 in. (15.2 cm) and 8 ft (2.44 m). Subsequently, correction factors are created in each case for each Montana flume under submerged conditions and the application of the factors is demonstrated. [ABSTRACT FROM AUTHOR]

Calibration of gates under free-flow and submerged-flow regimes is a classical hydraulic problem. In this paper, dimensional analysis was applied to investigate both free- and submerged-flow conditions through a radial gate. The original Ferro's method for submerged flow regime was modified by introducing the maximum allowable tailwater depth permitting free flow. Based on the Buckingham theorem and applying the incomplete self similarity (ISS) concept, different forms of the dimensional equations were proposed. According to the current available experimental data, the most accurate dimensionless formula was proposed. The proposed dimensional equation not only is more accurate than the original Ferro's method but can also be applied for free- to submerged-flow conditions continuously and through the transition zone. Finally, a new discharge reduction function (DRF), which is applicable for other water measuring structures and gates working under submerged flow condition, was identified. [ABSTRACT FROM AUTHOR]

Submerged sluice gates may be used as discharge measuring structures in irrigation channels. One commonly used model to predict discharge under submerged gates is based on the simultaneous solution of the energy and momentum equations (EM method). The conventional assumption for the solution is that the roller forming downstream of the gate is a static bubble of water with zero net flux of both momentum and kinetic energy. Energy losses along the submerged gate flow are commonly neglected. In this study, rational analysis of the EM method shows that the roller momentum flux and the energy loss may be considerable. A novel formulation of the EM method accounting for these two phenomena is proposed. Although it yields results similar to those of the conventional method, the new method introduces rationality in the application of the EM equations for submerged gate flow and helped to critically revise the assumptions in which the conventional EM method is based. [ABSTRACT FROM AUTHOR]

Abstract: The flow movement through a sluice gate is investigated for both free and submerged flow conditions. For free flow condition, the current dimensionless formula, indicated acceptable accuracy; while for submerged flow condition it was modified especially for low submerged condition. In this regard, Buckingham theorem along with the Incomplete Self-Similarity concept was employed and a new stage–discharge relationship was developed accordingly. Also, to achieve a suitable formula for submerged flow condition being accurate in low submergence, the maximum tailwater depth allowing the free flow condition and head loss factor were identified as missing parameters in the functional dimensional equation. Based on employing these parameters the function of Discharge Reduction Factor (DRF) was defined. [Copyright &y& Elsevier]

Laboratory experiments of sediment entrainment were carried out in a flume for different flow configurations with particle image velocimetry (PIV) used to measure the flow velocity. The experiments were done in a low submergence condition. Measurements revealed that the vertical distribution of streamwise flow velocity at the instant of entrainment is significantly different from the temporal mean flow profile. The role of turbulence for a given flow depth is found to decrease with an increase in exposure of the particle. An expression for threshold velocity is proposed that accurately represents the enhanced near-bed turbulence during entrainment. A Shields-type parameter, expressed in terms of critical near-bed flow velocity rather than shear velocity, is used to define the sediment transport threshold. [ABSTRACT FROM AUTHOR]

Compared with traditional weirs, Jambor weirs have the advantage that they reduce afflux due to their hydraulically-optimized shape. Hence, for identical discharge capacity, the height of the gate and thus the cost are reduced significantly. Although Jambor weir sills have been used in a combination with movable weirs for decades, the relationship between sill height, headwater and tailwater conditions and the resulting discharge has so far not been investigated systematically. Based on extensive tests in a hydraulic flume, an empirical equation and a dimensionless design chart were developed to estimate the backwater effect in the design phase to achieve the highest possible weir sill with an optimum hydraulic performance. [ABSTRACT FROM AUTHOR]

A comprehensive experimental investigation was performed to better understand the effect of the weir geometry of a Piano Key weir (PKW) on the discharge coefficient for both free and submerged flow conditions. Experiments were conducted in a 12 m long, 0.4 m wide and 0.7 m deep rectangular glass-walled flume. The effects of the PKW geometry, including weir length and height, up- and downstream key widths as well as up- and downstream apex overhangs on the weir flow discharge coefficient were investigated, so that the governing weir head-discharge relationship resulted. In addition, on the basis of a comprehensive data set, practical discharge coefficient relations associated with the standard weir equation were proposed for both free and submerged flows over PKWs. The present correlations cover various types of PKWs. From the experimental data, optimum values of the primary dimensionless weir parameters result produce the maximum discharge efficiency. [ABSTRACT FROM AUTHOR]

The current design of bridge foundations based on equilibrium scour depths is much larger than the real maximum scour depth since peak flood periods are often too short to reach equilibrium conditions. Based on a tested hypothesis on the time rate of scour, this research presents a power-exponential equation for the time-dependent clear-water scour depth including a nonzero initial condition for submerged bridge flows. For zero initial conditions, the proposed equation is reduced to a log or power law during the initial phase and an exponential decay near the equilibrium condition. The proposed equation reduces design depths according to design flows and their peak periods, translating into significant savings in the construction of bridge foundations. With a real-time monitoring system, the proposed equation also predicts time-series scour depths during floods, helping bridge managers formulate timely corrective strategies. [ABSTRACT FROM AUTHOR]

The seasonal treatment efficiency of a pilot-scale constructed wetland system located outdoors in a semi-arid, temperate climate was evaluated for graywater in a comprehensive, 1-year study. The system consisted of two wetland beds in series—a free water surface bed followed by a subsurface flow bed. Water quality monitoring evaluated organics, solids, nutrients, microbials, and surfactants. The results showed that the wetland substantially reduced graywater constituents during fall, spring, and summer, including biochemical oxygen demand (BOD) (92%), total nitrogen (85%), total phosphorus (78%), total suspended solids (TSS) (73%), linear alkylbenzene sulfonate (LAS) surfactants (94%), and E. coli (1.7 orders of magnitude). Except for TSS, lower removals of graywater constituents were noted in winter—BOD (78%), total nitrogen (64%), total phosphorus (65%), LAS (87%), and E. coli (1.0 order), indicating that, although wetland treatment slowed during the winter, the system remained active, even when the average water temperature was 5.2 ± 4.5°C. [ABSTRACT FROM AUTHOR]

Abstract: Identifying the free or submerged flow condition and the threshold between the two regimes is vital for accurate flow measurement through a gate. In this paper, analytical findings about distinguishing condition curve of radial gates are presented. The generality of the available calibration methods of the radial gates has been analyzed. Then, based on the assumption of starting the transition zone right at the interception point of the free and submerged flow relationships, a comprehensive equation is developed to distinguish the flow condition through a radial gate. Using ample high quality available experimental data, the accuracy of the proposed distinguishing curve was verified. The results indicated that the proposed distinguishing curve accurately identified observed flow condition data. Finally, by defining a suitable sensitivity index, the effects of downstream channel width, energy loss through the gate, Reynolds number, and contraction coefficient on the distinguishing condition curve have been evaluated. Also, the results promise the application of the proposed method for situations where only one of some parallel radial gates is operating under the submerged flow condition. [Copyright &y& Elsevier]

The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face of the gate together with the energy equation. The contraction coefficient varies with the relative gate opening and the relative submergence, especially at large gate openings. The contraction coefficient may be similar in submerged flow and free flow at small openings but not at large openings, as shown by some experimental results. An application to discharge measurement is also presented. [ABSTRACT FROM AUTHOR]

Real accuracy of several calibration methods for sluice gates working in the submerged orifice flow condition was determined considering water discharge from water levels and gate openings. Data were taken from three gates of the same laboratory canal covering a large operational range. Using accurate hydraulic data, most of the methods produce errors of up to ±10%. However, errors can rise up to ±40% with methods using typically recommended calibration values or constant discharge coefficients. The best results were obtained by a method based on dimensional analysis and the incomplete self-similarity theory proposed recently in the literature. Calibration with field data, in this case, produced errors not higher than ±3%. On the other side, when the gate discharge data are not available, the use of a contraction value of 0.611 within a good theoretical formulation gives very good results. [ABSTRACT FROM AUTHOR]

This paper discusses the capability of Guo et al.'s (2021) equations to determine the discharge of radial gates under submerged flow conditions. It was concluded that Guo et al.'s (2021) equations are associated with error reduction compared to the Incomplete Self-Similarity (ISS) theory and the calibration method. However, it does not have a significant advantage over Energy-Momentum (E-M) approach. Employing E-M principles, new equations were proposed to determine the discharge of radial gates, which has some advantages compared to Guo et al. (2021), such as (1) error reduction under partially and fully submerged flow conditions, (2) least dependence on the empirical constants, (3) uniformity of form over the entire submerged condition, and (4) no need to classify the submerged flow. Field calibration showed that the proposed equations in the present study for a single gate predict the discharge of parallel radial gates with a mean absolute error of less than 4.5% subject to the submerged operation of all open gates. • Evaluation of Guo et al.'s (2021) equations with pre-proposed methods to predict the discharge of radial gates. • Deducing a novel theoretical equation for estimating the discharge of radial gates with the least empirical constants. • Field verification of single-gate equations to predict the discharge of multi-radial gates. [ABSTRACT FROM AUTHOR]

The article proposes a mathematical model of an automatic upstream water level control gate designed to operate under free and submerged flow conditions, called the Vlugter gate. This automatic gate controls the upstream level close to a design level, using a counterweight to compensate for the hydraulic pressure on the gate. The proposed gate model is an extension of an existing model for free flow conditions (Begemann gate) to submerged conditions. Submergence effects are introduced both in the discharge law and the equilibrium law. The mathematical model is validated on experimental data from two small-scale gates and on data from literature, in order to show the ability of the model to simulate the behavior of gates of various dimensions. [ABSTRACT FROM AUTHOR]

Submergence is defined as the ratio of the tailwater to the headwater, both measured relative to the weir crest. The performance of published submerged ogee-crest head-discharge relationships was investigated in this study. Four submerged and one free-flow head-discharge relationship were evaluated relative to a submerged ogee-crest data set covering a range of tailwater elevations, discharges, and weir geometries. For submergence levels <0.70, the head-discharge relationship was relatively independent of the tailwater elevation, but at higher submergence levels, this was not the case. For submergence values <0.8, the submergence head-discharge data were best predicted using the free-flow head-discharge relationship. For submergence values >0.8, the accuracies of all but one of the head-discharge relationships were very poor. For such high submergence levels, more accurate methods are needed for predicting submerged ogee-crest head-discharge relationships. [ABSTRACT FROM AUTHOR]

We investigate the turbulent structure of shallow open channel flows where the flow depth is too small (compared with the roughness height) to form a logarithmic layer but large enough to develop an outer layer where the flow is not directly influenced by the roughness elements. Since the log layer is not present, the displacement height d, which defines the position of the zero plane, and the shear velocity u* cannot be found by fitting the velocity data to the log law. However, these parameters are still very important because they are used for scaling flow statistics for the outer and roughness layers. In this paper we propose an alternative procedure for evaluating d in laboratory conditions, where d is found from additional experiments with the fully developed log layer. We also point out the appropriate procedure for evaluating the shear velocity u* for flows with low submergence. These procedures are applied to our own laboratory flume experiments with uniform sphere roughness, where velocities were measured using Particle Image Velocimetry. Results were interpreted within the framework of the double-averaged Navier–Stokes equations and include mean velocities, turbulence intensities, Reynolds stresses, and form-induced normal and shear stresses. The data collapse well and show that in flows without a developed log layer the structure of turbulence in the outer layer remains similar to that of flows with a log layer. This means that even though the roughness layer in the experiments reported herein was sufficiently high to prevent the development of the log layer, influence of the bed roughness did not spread further up into the outer layer. Furthermore, the results show that flow statistics do not depend on relative submergence except for the form-induced stresses which increase when relative submergence decreases. [ABSTRACT FROM AUTHOR]

In this paper, we study the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal. The analytical approach of Liu et al. in 2004 for solving wave amplification around a circular island mounted on a shoal is extended in this study to investigate waves above a submerged shoal. In this approach, the mild-slope equation is first transformed into an explicit equation by using Hunt’s 1979 Padé approximation to the wave dispersion equation. It is then solved analytically in terms of combined Fourier series and Taylor series. For incident waves varying from short to long waves, wave amplifications in the vicinity of the shoal are calculated using the newly derived analytical model and they agree excellently with the finite difference solutions of Lin in 2004. It is found that, for the particular shoal studied in this paper, there exists an energy focal point where the wave amplitude is the maximum. This point is the result of combined wave refraction, diffraction, and reflection. The point is always located along the x-axis and it is behind the shoal center for very short waves. As the increase of wave period, it moves upstream and it can come in front of the shoal center for very long waves when wave reflection is significant. For a particular incident wave, wave amplification increases and the focal point moves toward the shoal center with the reduction of the water depth above the shoal center. The maximum wave amplitude increases exponentially as the decrease of local water depth. It is also found that there exists the so-called “calm” areas for shallowly submerged shoal, which are located behind the focal point and the local amplitude can be as small as nearly zero. [ABSTRACT FROM AUTHOR]

Data obtained from two physical models were compared to the results obtained from numerical model investigations of two ogee-crested spillways. In 2001, Savage and Johnson investigated ogee-crested spillways without the effect of tailwater; the present study includes the influence of tailwater on the spillway. The comparison showed that numerical modeling can accurately predict the rate of flow over the spillway and the pressure distribution on the spillway. The results of this study provide users of numerical models performance information that can be used to aid them in determining which tool to use to effectively analyze dams and their associated spillways. [ABSTRACT FROM AUTHOR]

Dimensional analysis was used to obtain stage–discharge relationships under submerged and free flow conditions in radial gates to develop a management tool. Experimental data from a laboratory flume and the indicial method of dimensional analysis were used for this purpose. The resulting equation relates the discharge (or critical depth) to upstream and downstream water depth and gate opening. These equations were then validated by experimental data obtained from field radial gates and compared with the conventional gate equation. Results showed that there was a good agreement between dimensionless equations and field and laboratory data under submerged or free flow conditions. Dimensionless equations are more general and accurate than the conventional ones when there is not an accurate estimation of discharge coefficients. [ABSTRACT FROM AUTHOR]

The energy-momentum (E-M) method for calibrating submerged radial gates was refined using a large laboratory data set collected at the Bureau of Reclamation hydraulics laboratory in the 1970s. The original E-M method was accurate in free flow, and when the gate significantly controls submerged flow, but for large gate openings with low head loss through the gate, discharge prediction errors were sometimes large (approaching 70%). Several empirical factors were investigated with the laboratory data, including the combined upstream energy loss and velocity distribution factor and the submerged flow energy correction. The utility of the existing upstream energy loss and velocity distribution factor relation was extended to larger Reynolds numbers. The relation between the relative energy correction and the relative submergence of the vena contracta was shown to be sensitive to the relative jet thickness. A refined energy correction model was developed, which significantly improved the accuracy of submerged flow discharge predictions. Although the focus of this work was radial gates, the energy correction concept and these refinements potentially have application to all submerged sluice gates. [ABSTRACT FROM AUTHOR]

The main research objective consisted in analysing the influence of roughness caused by aquatic vegetation (av), in particular submerged macrophytes, on the overall flow field. These plants are highly flexible and behave differently depending on the flow situation. They also react substantially to the flow field and thus, the roughness becomes variable and dynamic. Conventional flow formulas, such as the Manning or the Strickler formula, are one-dimensional and based on integral flow parameters. They are not suitable for quantifying the roughness of av, because the flow is complex and more dimensional due to the variable behaviour of the plants. Therefore, the present investigation concentrates on the definition of a characteristic hydraulic roughness parameter to quantify the resistance of av. Within this investigation laboratory experiments were carried out with three different types of av, chosen with respect to varying plant structures as well as stem lengths. Velocity measurements above these plants were conducted to determine the relationship between the hydraulic roughness and the deflected plant height. The deflected plant height is used as the geometric roughness parameter, whereas the equivalent sand roughness based on the universal logarithmic law modified by Nikuradse was used as hydraulic roughness parameter. The influence of relative submergence on the hydraulic roughness was also analysed. The analysis of the velocity measurements illustrates that equivalent sand roughness and zero plane displacement of the logarithmic law are correlated to the deflected plant height and are equally to this height. [Copyright &y& Elsevier]

Weirs are one of the most common hydraulic structures used to regulate the upstream approach flow depth and measure the flow discharge. The hydrofoil weirs are a type of short-crested weirs that are designed based on the airfoil theory. These weirs have some merits compared to other types, such as a higher discharge coefficient, more stability, better submergence limiting condition, and lower fluctuations of the pressure and the free-surface profile. In the present study, experimental models of hydrofoil weirs with different relative eccentricities, cambers, angles of attack, and upstream slope angles are applied to investigate their hydraulic characteristics under free and submerged flow conditions. The longitudinal profiles of static pressure over different hydrofoil weirs are compared to circular-crested and ogee weirs. The results indicate that the maximum bed negative pressure belongs to the circular-crested weir, and the lowest bed pressure over the hydrofoil and ogee weirs are approximately the same. Applying a hydrofoil weir with an appropriate curvature and angle of attack instead of a circular-crested weir not only increases the structural weir height as well as the upstream water depth but also results in the lowest values of bed negative pressure, thereby reduces the potential of cavitation over the weir body, being safer hydraulic structures. The results also show that the discharge coefficient of hydrofoil weirs is greater than that of the broad- and short-crested weirs for the upstream approach flow depth relative to the weir crest to weir length h 1 / L > 0.12 and is greater than that of the ogee weirs for 0.35 < h 1 / L < 0.45. Furthermore, the derived relationships for the discharge coefficient, threshold submergence, and the discharge reduction factor due to submergence accurately predict the hydraulic characteristics of hydrofoil weirs compared to the available developed empirical relationships for these weirs and can be used efficiently for design purposes. • Hydraulic characteristics of hydrofoil weirs are investigated under free and submerged flow conditions. • The lowest bed pressure over the hydrofoil and ogee weirs are approximately identical. • Applying a hydrofoil weir with an appropriate curvature and angle of attack results in the lowest bed pressure. • The discharge coefficient of hydrofoil weirs is greater than that of the other types of weirs. • The present relationships precisely predict the hydraulic characteristics of hydrofoil weirs. [ABSTRACT FROM AUTHOR]

Sophisticated stage-discharge rating curves for radial gates are essential to modernization efforts in water conservancy and irrigation projects. However, it is a challenging hydraulic issue to accurately determine discharges through radial gates, especially when subjected to highly submerged flow conditions. According to the variation trend of jet Froude number and the mechanism of energy dissipation subjected to submerged flows, a new criterion was proposed to subdivide submerged flow into partially submerged and totally submerged flows. Thus, the three stage-discharge equations were developed for free flow, partially submerged flow and totally submerged flow, respectively. With the aid of the experimental data of single radial gate and the field data of multi-radial gates, the proposed discharge calibration method, referred to as the identification method, was tested and verified. The results indicated the discharge prediction accuracies were satisfactory, in which the mean absolute percentage errors were less than 10%. The proposed method is feasible and easily programmed. • Submerged flows through gates are classified as partially and totally submerged flow conditions. • Jet Froude numbers are important indicators to distinguish submerged flow conditions. • Variations of jet Froude number are related to both relative gate openings and submergence ratios. • Stage-discharge relationships should be calibrated for parallel radial gates in practice. [ABSTRACT FROM AUTHOR]

In this study, the flow through a simple low-cost flume constructed using two semi-cylinder contractions on either side of a rectangular channel was experimentally investigated. In practice, these flumes may operate under free- or submerged-flow conditions depending on the downstream flow depth. To reliably estimate the flume discharge, free- and submerged-flow conditions should be accurately distinguished. At present, there is no equation to estimate the submergence threshold. This study investigates the possibilities of using these flumes under submerged-flow conditions. The discharge of the submerged flume may be calculated on the basis of the free-flow discharge equation. Thus, two new free-flow discharge equations were deduced: a general equation by considering the contraction ratio with an average error of 2.25%, and another one by neglecting it with an average error of 4.88%. Compared with the existing discharge equations, the proposed free-flow equations are the best ones. Under submerged-flow conditions, the submergence ratio affects the flow discharge. Using the measurements carried out in this study, the submergence threshold ratio and submerged-flow discharge were formulated and calibrated with the average errors of 2.96% and 3.80%, respectively. The equation to distinguish the free- and submerged-flow conditions was also deduced by equating the submerged- and free-flow discharge equations yielding a novel real solution. • Experimental study of a simple flume constructed using two semi-cylinder contractions. • Whilst most studies limit to free flow conditions, this study focuses on submerged flows. • Deducing discharge relations under both free and submerged flow conditions. • Deducing curve distinguishing free-flow and submerged-flow conditions. • Submergence threshold ratio depends on upstream depth ratio and varies in range of 76–94%. [ABSTRACT FROM AUTHOR]

A new design of a labyrinth weir is introduced in this study by adding a square pool to the vertex of a one-cycle triangular labyrinth weir with a sidewall angle of 45°. The addition of the square pool increased weir length without causing an excessive nappe interaction, and as a result, reduced the head water over the weir with the same discharge. Laboratory experiments were carried out to investigate the hydraulic performance of the new design with a potential application in pool-weir fishways. Mean and turbulence characteristics of flow for different weir geometries and in both free and submerged flow regimes were measured to be used for prediction of fish behaviour in the upstream of the proposed weir models. Discharge coefficients based on channel width and weir length were calculated. It was found that the new design can significantly increase the capacity of triangular labyrinth weirs and provide financial advantages in construction over triangular labyrinth weirs without pools in low discharges. In submerged flow conditions, the proposed model performed better than sharp-crested linear weirs in low discharges. Contour plots of the three-dimensional velocity components showed a region of strong mean flow around the neck of the new weir model. Turbulent characteristics such as turbulent kinetic energy, power spectra, exuberance ratio, and joint probability distribution functions of velocity fluctuations were extracted from instantaneous three dimensional velocities for different weir depths and flow regimes. Two vertical planes were identified based on the highest turbulent mixing in free and submerged flow regimes. The depths contributing the most to turbulent mixing were identified; active depths decreased as the flow regime changed from free to submerge flow regime. • A new design of triangular labyrinth weir is introduced. • Discharge capacity of the new design is higher than the common triangular for h o / P ≤ 0.35. • Negative modular limits were observed for h o / P ≤ 0.3 due to formation of surface jets. • A dominant frequency of 0.2 Hz was obtained for the longitudinal and vertical velocity signals. • Strong mixing zones were found in the neck of the weir with ERmin = 1/6. [ABSTRACT FROM AUTHOR]

Gates are simple hydraulic structures which have been widely used for flow control and measurement in irrigation networks. In this paper new sluice gates with cylindrical and semi-cylindrical edges were introduced and the flow movement below these types of gates was experimentally investigated for both free- and submerged-flow conditions. The Buckingham theorem of dimensional analysis and the self-similarity theory were applied for developing the stage-discharge relationships for the two investigated flow conditions. For these cylindrical and semi-cylindrical edged gates and a free-flow condition, the proposed stage-discharge relationship was characterized by an estimate error less than or equal to 5% for 96.0% and 93.7% of the calculated values, respectively. Finally, an equation for calculating the maximum tail water depth allowing free flow condition was proposed. • Cylindrical and semi-cylindrical edged sluice gates are experimentally investigated. • Theoretical stage-discharge equation is deduced for free and submerged-flow condition. • The theoretical stage-discharge relationship is calibrated by flume data. • Maximum tail water depth allowing free flow condition is determined. [ABSTRACT FROM AUTHOR]

This work presents a critical analysis of submerged flow over rectangular weirs of finite crest length. For finite crest length weirs, because the existing data sets are not extensive, new experiments for these weirs with sharp-edged and rounded crest were conducted. Based on these data, a diagram is developed to show the variation of the normalized tailwater depth with where is the free flow head and is the length of the crest, to predict the onset of submergence or the modular limit. Water surface profiles of flow over weirs of finite crest length with square-edge and rounded crests were plotted to study the formation of waves in modular and submerged conditions. Characteristics length scales such as wave length and amplitude at the modularity limit and the location of the first trough downstream of the weir were measured to generalize surface profiles at different flow discharges. An empirical equation for the discharge reduction factor was also formulated. This equation has two exponents with different values for several classes of finite crest length weirs with either square edged or rounded crest. [ABSTRACT FROM AUTHOR]