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Sluice gates are commonly used to measure water discharge and to adjust the water level in open canals. Sluice gates can also be used at the crest of dam spillways for controlling floods. Estimation of head loss (∆E/E₀) and discharge coefficients (C_d) 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 C_d for sluice gates, a comprehensive literature review shows that there are no studies of ∆E/E₀ (to the best knowledge of the authors). Knowledge of ∆E/E₀ is necessary for the design of intakes and irrigation canal inverts. This study uses the physical model of sluice gate to introduce helpful charts for energy loss estimation. Experiments were conducted in the University of Tabriz, department of water engineering. A rectangular canal with length of 12 m, width of 0.5 m and height of 0.8 m was used. Vertical slide gate was installed at the 6 m from canal inlet to permit flow become uniform. Water circulation is carried out using a submerged pump. Water is pumped in a 4.5 m head tank and then inters to canal with pipes. Water level/depth was measured with a point gauge with 0.1 mm accuracy. Discharge was measured with a calibrated rectangular sharp crested weir. Experiments were carried out with different discharges and gate opening. Results show that ∆E 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 (∆E/E₀) 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. The relative energy loss changed from the minimum value of 0.271 to the maximum value of 0.604. Multivariate regression method was used to calculate the relative energy loss and the average of the residuals was -0.004. The maximum and minimum residuals for ∆E/E₀ are 5 and -0.31, respectively. A mathematical equation with a coefficient of determination of 0.925 was presented to separate the boundary of free flow from submerged flow. To estimate the discharge coefficient in submerged flow, a mathematical equation was obtained. For this equation, the average of the residuals was -0.004. The maximum and minimum residuals for the discharge coefficient are -0.084 and 0.116, respectively. Application of multiple non-linear regression (MNR) models are presented for predicting ∆E/E₀ and C_d. The high energy losses cannot be ignored in intake structures and canal designing processes. Their impact on minor canal inverts receiving water from main canals should be considered. Application of MNR was presented from a simple equation to more sophisticated equations by improving regression relations in each step. The MNR method provides accurate equations for predicting performance for both ∆E and C_d.

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Abstract :Side sluice gates are flow metering structures, which are used for controlling the flow from the main channel to the side channel. It is usually required to determine the discharge coefficient for estimation of the side sluice gate discharge. In order to study the influence of some important parameters on the discharge coefficient of side sluice gate, extensive experiments were conducted. The experiments were conducted in a re-circulating channel having a central angle of 180o, a centerline radius of RC = 2.6 m, and the width and height of 0.6 m. The ratio of radius of centerline of the channel to the width of the channel Rc/B was 4.33. The bend was connected to two straight upstream and downstream reaches. The upstream one was 7.2 m in length while the length of downstream one was 5.2 m. The bed and sides of the channel were made of glass and supported with metal frames. The side channel was set at different locations of bend (i.e. at the sections 53, 65, 90, 115 and 135 degree). The side sluice gate was made of Plexiglas and was set at the entrance of the side channel. The experiments were carried out for different gate openings, upstream depth of flow and location of the side sluice gate under free flow condition. The upstream discharge was measured by a digital flow meter, while the downstream discharge was measured using a calibrated triangular weir. The difference of upstream discharge and downstream discharge resulted to the sluice gate discharge. The results of experiments on a side sluice gate located in a 180 degree curved channel are reported. The variation of flow depth along the side sluice gate was studied. The influence of different parameters like: depth of flow, approach Froude number, side sluice gate opening and location of side sluice gate on discharge coefficient were investigated. It was found that increase of approach Froude number increases the discharge coefficient. Moreover, increase of relative flow depth h1/a increases the discharge coefficient. Here, h1 is the approach Froude number and a is the sluice gate opening. Maximum discharge coefficient was observed when the sluice gate was located at the section 150 degree in the channel bend. New equation for discharge coefficient of a side sluice gate in a 180 degree curved channel was developed. The discharge coefficient was found to be related to approach Froude number, location of sluice gate in the channel bend and the relative flow depth

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The present paper discussed about the technique that can be used to vector the exhaust flow in the pitch directions with using Double Throat nozzle (DTN). Compressible and supersonic gas flow inside a Double Throat nozzle and its exhaust plume at specific nozzle pressure ratios have been numerically studied with several turbulence models. The numerical results reveal that, the SST k–ω model gave the best results compared with other models in time and accuracy. In the present research, effects of changes in injection area of secondary flow and percent of secondary mass flow rate, on performance of Double Throat nozzle and thrust vectoring system have been investigated. The predicted results show that by decreasing the value of secondary flow injection area in a case with 7% secondary injection, the thrust vector angle increase 18º to 21º and thrust vectoring efficiency will increase. But by decreasing the value of secondary flow injection area, the thrust and discharge coefficient will decrease. Also when secondary mass flow rate increases, the discharge coefficient will decrease. So that in the design of fluidic thrust vectoring with double throat nozzle, the value of secondary mass flow rate should be low.

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Weirs possess an essential role in dam safety and should spill floods with high return period. The designers can enhance the width of the weirs to increase the discharge capacity. But this has sometomes topography and economic limitations. Arced weirs can be considered as an alternative. A arced weir is a arcuate of a circle in plan-view that provides an increase in crest length for a given channel width that increas the flow capacity for the same head. Also when modification and capacity increase in existing spillways are necessary, this structure is recommended. In this paper, the hydraulic performance of arced weirs located in a reservoir has been studied experimentally. Firstly, dimensionless parameters affecting the performance of arced weirs is introduced using Buckingham π theorem. Then effect of arc angle (θ) and head water ratio (H0/P) on hydraulic performance of arced weirs was experimentally investigated and hydraulic performance of the tested arced weir geometries was compared with a linear configuration. For this purpose, Arches with different radius of curvature from linear to semi-circular configurations ( ) and various head water ratio Were studied. To simulate reservoir conditions, a reservoir simulator was designed and built. Laboratory observations show that the converging of flow over a arced weir causes a locally bulge in the downstream of the weir. This phenomenon was named as flow mound. Results show that arc angle (θ) and head water ratio (H0/P) have a direct effect on the flow mound and an increase in each of them leads to mound height rise. The head-discharge relationship for arced weirs was determined by using a general form of the rectangular weir equation. Data from physical models were used to determine discharge and upstream head for the flat crested weirs installed in the reservoir. from discharge curves, it was found that with increasing angle of weir, that provide an increase in crest length for a given channel width, flow capacity increases for a given upstream head. Discharge coefficients as a function of H0/P for arced weirs are also presented and is compared with linear configuration. The results show that with increasing H0/P, discharge coefficient is declined for each tested configuration. Also with increasingθ , that leads to greater convergence of flow passing over the weirs, discharge coefficient decreases. Efficiency parameter is defined as the ratio of discharge of arced weir to that of liner weir with a same width. From efficiency curves it can be understood that the semi-circular weir can improve efficiency up to about 45%. However for all tested weirs , efficiency decreases with increasing H0/P and it gets close to 1. Finally, based on the results and limitations of this study, a methodology for the design of arced weirs located in the reservoir is presented. By using this method, the geometric parameters if an arced weir that is able to pass a certain flow rate for a given hydraulic head, will be determined.

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Abstract:
Modern horseshoe spillways are combination of external and internal weirs and determination of hydraulic parameters of this kind of spillways is essential. In this study, by making physical models of Modern horseshoe spillway in laboratory dimension, some hydraulic parameters of modern horseshoe spillways like discharge coefficient, discharge rate through the two weirs and water surface profiles in different parts of horseshoe weir are investigated. The results showed that by increasing the ratio of head (h) to external weir’s Length (Lw) for Lw≤100 cm, the discharge coefficient for internal weir (CO) increases linearly. By increasing ratio of internal weir discharge to external weir discharge Q1/Q2, the discharge coefficient has a decreasing trend between 0.65 to 0.3 . By increasing the external weir length, the discharge rate through external weir increases while it decreases in internal weir. The external weir with Lw=100 cm has better performance than other Lws and If we select it as the better length, on average 31 percent of the flow will pass from the internal weir. Classic and Modern horseshoe spillways are able to reduce the head above the weir respectively to 28 and 50% in comparison to rectangular weir head with the same width. Investigation of the water surface profiles shows that by creating an internal weir, rooster tail hydraulic jump that existed in Classic horseshoe spillway is removed.

Keywords: Modern & Classic horseshoe spillway, Discharge coefficient, Internal weir, Physical model.


Abstract:
Modern horseshoe spillways are combination of external and internal weirs and determination of hydraulic parameters of this kind of spillways is essential. In this study, by making physical models of Modern horseshoe spillway in laboratory dimension, some hydraulic parameters of modern horseshoe spillways like discharge coefficient, discharge rate through the two weirs and water surface profiles in different parts of horseshoe weir are investigated. The results showed that by increasing the ratio of head (h) to external weir’s Length (Lw) for Lw≤100 cm, the discharge coefficient for internal weir (CO) increases linearly. By increasing ratio of internal weir discharge to external weir discharge Q1/Q2, the discharge coefficient has a decreasing trend between 0.65 to 0.3 . By increasing the external weir length, the discharge rate through external weir increases while it decreases in internal weir. The external weir with Lw=100 cm is the optimum length and If we select it as the optimum length, on average 31 percent of the flow will pass from the internal weir. Classic and Modern horseshoe spillways are able to reduce the head above the weir respectively to 28 and 50% in comparison to rectangular weir head with the same width. Investigation of the water surface profiles shows that by creating an internal weir, rooster tail hydraulic jump that existed in Classic horseshoe spillway is removed.

Keywords: Modern & Classic horseshoe spillway, Discharge coefficient, Internal weir, Physical model.
Keywords: Modern & Classic horseshoe spillway, Discharge coefficient, Internal weir, Physical model.Keywords: Modern & Classic horseshoe spillway, Discharge coefficient, Internal weir, Physical model.Keywords: Modern & Classic horseshoe spillway, Discharge coefficient, Internal weir, Physical model.Keywords: Modern & Classic horseshoe spillway, Discharge coefficient, Internal weir, Physical model.

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Weirs have important roles in dam safety in which they should spill floods with high return period. Designers generally enhance width of the weirs to increase their discharge capacity. This procedure involves topography as well as economic limitations. Here, arced weirs can be considered as an alternative. In plan view, arced weir is part of a circle that increases the crest length for a given channel width. This increases the flow capacity at a similar heads. Such structures are also recommended for modification and increasing the capacity of the existing spillways. Discharge capacity of labyrinth weirs is a function of flow height, effective crest length, height of weir and shape of the crest. Discharge coefficient is also a function of height of flow, height of weir, weir thickness and crest shape. In this study, hydraulic characteristics of arced labyrinth spillways are numerically investigated. Here, the effect of crest shape on the discharge coefficient of the labyrinth spillway is included. In the first step, dimensionless parameters affecting the performance of arced weirs are introduced using Buckingham π theorem. To analyze this problem, a commercially available CFD code; Flow 3D by Flow Science; was selected. Flow 3D is known for its ability to accurately tracking free surface using Volume of Fluid (VOF) method. A similar method called Fractional Area to Volume Ratio (FAVOR) is used to define labyrinth within the model. Also, Reynolds averaged Navier Stokes (RANS) equations are solved using a finite volume method. Besides, The Renormalized Group Theory (RNG) model was implemented for turbulent simulations. The laboratory data of Crookston and Tullis (2012a) is used to validate the numerical model. These researchers conducted experiments on physical modeling of the labyrinth spillways at the Utah Water Research Laboratory at Utah State University. Comparison of numerical simulations with those of experimental results validates the ability of this software to simulate the complex flow over labyrinth spillways with an acceptable accuracy. In this study, result of 16 geometry models was used to develop a hydraulic design and analysis formulation for arced labyrinth weirs. Discharge coefficient data for Half-Round, Quarter-Round, Sharp-crest and Flat-crest arced labyrinth weirs are presented for 6̊ ≤ sidewall angles ≤ 24̊ and various head water ratio (0.1≤ H0/P ≤ 0.9). The study has shown that half round crest shape could increase the discharge coefficient about 22% compared to other crest shapes. Also, the results show that factors such as local submergence and nappe interference near an upstream apex has a negative impact on performance of arced labyrinth weirs. The local submergence area is directly related to the flow head, crest shape and sidewall angle. For high head conditions, the local submergence may decrease the efficiency of a labyrinth spillway. Efficiency parameter is defined as the ratio of discharge of arced weir to that of liner weir with the same width. From efficiency curves indicates that reduce of sidewall angle can improve efficiency. As a result, the highest efficiency related to arced labyrinth spillway with sidewall angle (α = 6̊ ).

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Spillways and bottom outlets are the common hydraulic structures in dam engineering to convey excess water from the reservoir toward the downstream river. Economy and operation are the major factors affecting the type of spillway and its’ crest shape to avoid unfavorable hydraulic phenomena. An appropriate spillway crest results in increasing the discharge coefficient and distributing a uniform pressure inside the conveying conduits. One of the most common types of spillways in dam engineering is shaft spillways with morning glory inlet. Generation of swirling flow at the entrance of the shaft spillways and entraining air into the conduits is an unfavorable phenomenon. Air-entrainment into the system leads to different depressing effects on system operation including reduction of the discharge coefficient and can cause severe damages. To control the swirling flow phenomenon one way is the application of anti-vortex devices. Applying certain shape of inlets e.g. installing a Daisy (Marguerite)-shape inlet over the shaft entrance is another alternation to avoid the swirling flow effects thereby to increase the discharge coefficient. Marguerite-shape inlet has been used in different existing dam projects. Marguerite inlet is a unique inlet compared to other shapes of spillway crests for a constant head. This is in part due to spatially varied flow inside the marguerite inlet which makes it capable of passing greater discharge. Although different types of dam spillways have been the subject of different investigations, there is a lack of study on these types of spillways.
In this study, the effects of Daisy (Marguerite)-shape inlet on free-flow through shaft spillways have been investigated based on model experimentation. Dimensional analysis has been used to determine the effective dimensionless parameters. Experiments were conducted in a cylindrical model of 2 m diameter with two shafts of 10 and 12.5 cm diameters on the tank bottom. The tests have been performed based on a wide range of geometric and hydraulic parameters to study the effects of each dimensionless parameter on flow hydraulics. Finally, applying SPSS software and nonlinear regression analyses empirical correlations were obtained for estimating the discharge coefficient and the threshold depth of orifice flow over Daisy-shape inlets. To validate these correlations, the normalized root-mean-square error (NRMSE), the weighted quadratic deviation (WQD) and the coefficient of determination R2 were applied. Contrary to R2, both NRMSE and WQD must be small to have the best correlations.
Spillways and bottom outlets are the common hydraulic structures in dam engineering to convey excess water from the reservoir toward the downstream river. Economy and operation are the major factors affecting the type of spillway and its’ crest shape to avoid unfavorable hydraulic phenomena. An appropriate spillway crest results in increasing the discharge coefficient and distributing a uniform pressure inside the conveying conduits. One of the most common types of spillways in dam engineering is shaft spillways with morning glory inlet. Generation of swirling flow at the entrance of the shaft spillways and entraining air into the conduits is an unfavorable phenomenon. Air-entrainment into the system leads to different depressing effects on system operation including reduction of the discharge coefficient and can cause severe damages.

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Labyrinth weir is one of the approaches to increase the discharge capacity. An arced ‎configuration improves the orientation of the labyrinth weir cycles to the approach flow and ‎increases the weir crest length for a given width. In this study, the effects of the entrance flow ‎conditions on the hydraulic‏ ‏performance of the arced ‎labyrinth weirs is studied experimentally.‎‏ ‏The effects of the angle between the entrance channel walls (Θ′) on the discharge coefficient ‎and the efficiency are investigated for different values of the ‎headwater ratio (Ho/P), the ‎downstream sidewall angle (α), and the weir arc ‎angle (Θ).‎ Experiments were conducted in a recirculating flume‏ ‏which is 10 m long, 2 m wide, and 0.9 m ‎deep at Tarbiat Modares University. To simulate the reservoir conditions, a specific setup was ‎added to the flume, known as the reservoir simulator. The flume was launched from its two ends ‎by two pipelines. The inflow passes from underneath of the reservoir simulator and enters into it ‎through a semi-circular opening in its horizontal‏ ‏wall. After moving‏ ‏over the horizontal‏ ‏wall, the ‎flow comes up through the gap between the vertical wall. Finally, it flows on the platform and ‎moves towards the downstream channel. All the plates (including the platform and the simulator ‎walls) have a semicircular plan-view with a porosity equal to zero. The‏ ‏weirs were mounted on ‎the platform at the entrance of the downstream channel. Totally 132 experiments were ‎conducted to investigate the effects of the mentioned parameters on hydraulic performance of ‎arced labyrinth weirs.‎ Due to the nappe interference, the local submergence forms in the downstream of the ‎labyrinth ‎weirs. The size‎ of local submergence regions increase by increasing the ‎headwater ratio ‎and the arc angle. However, vice versa trend occurs with the downstream sidewall angle. In ‎addition, for low values of the arc angle, the lateral flow from the side cycles to their adjacent ‎cycles produces the surface turbulences. The results ‎indicate that the discharge coefficient ‎decreases by increasing the ‎headwater ratio and the downstream sidewall angle. For low values ‎of the ‎headwater ratio, the discharge coefficient increases when the arc angle increases. ‎However, a decreasing trend is observed in high head conditions. By increasing the ‎arc angle ‎and decreasing the downstream sidewall angle, the efficiency of a labyrinth weir can be ‎increased. However, the efficiency gains diminish by increasing the ‎headwater ratio.‎ The efficiency of a labyrinth weir can slightly be increased by projecting of the cycles into a ‎reservoir for low values of Ho/P, α, and Θ. However, in the wide range of the research domain, ‎the efficiency decreases‏ when ‏the angle between the entrance channel walls increases. ‎According to the results of this research, the efficiency of a labyrinth weir can be increased up ‎to 20% by channelizing abutments in high head conditions. However, the effect of Θ′ is ‎insignificant for higher values of Θ. In addition, as α decreases, the benefits and the losses of ‎decreasing Θ′ become more ‎severe at higher and lower values of Ho/P, respectively.‎

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One of an effective and economical solution in order to weir efficiency is using nonlinear weirs, Which can cause  the increase of the flow over weir by changing in geometric plan and increasing in weirs length in fixed widths of the channel . in this research, the hydraulic performances of  the piano-key weirs has been simulated by FLOW-3D and also it has been validated by the laboratory data. In the following, the discharge coefficient (C_d) has been measured and evaluated with the creation of single and double circular orifice on the heel of weir ( , For the different water head and in relation to without dimension parameters    .
Findings shown with the expansion orifice diameter, discharge coefficient of combined weir -with the maximum opening  - is increasing between 0.5 to 6% in comparison to without orifice piano-key weir., besides, with the rise in the high of single orifice ,which has a fixed diameter, the discharge coefficient is reducing between 0.5 to 3%. From the other side, the usage of double orifices decreases the discharge coefficient in comparison to the single type at the same opening size, in a way that by increase in the distance of orifices, at first, it faces to the rising trend and then by reaching to   it starts revising. Finally, an equation is provided for the estimation of the discharge coefficient by benefiting without dimension parameters with   .
 

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In this paper hydraulics and flow structure over the rectangular piano key weirs with different heights have been studied experimentally and numerically and effects of different fillet shapes on hydraulic performance are investigated. Experiments are conducted in a one meter width flume. Models of the tested weirs are made from PVC Plates in 3 different heights and with the same L/W ratios equal to 5. Discharge coefficient curve for wide range of heads over height ratio for 3 different weir heights are determined and effect of triangular, half round and oval fillets on increasing of discharge coefficient are investigated. In this research, the chosen range for ratio of head over height is in good agreement with ratio which has been used to design of prototype weirs. Large triangular and oval shaped fillets have significant effects on improvement of performance of the piano key weirs. Main effect of fillets is more uniformly distribution of the flow streamlines over the downstream part of the side crest. In second part of this paper, one and half-key piano key weirs with oval noses and without any nose (net) have been numerically modeled using Flow-3D model. Discharge coefficients of one of the numerically simulated rectangular models is compared with derived discharge coefficient curve from physical model. Convergence of inflow and outflow of numerical model has been controlled. Satisfactory correspondence presents between the experimental and numerical studies. Discharge distribution over the crest of the normal PKW and the weir equipped with oval fillet are compared. Result showed that due to uniformly distribution of the streamlines, the fillet notably increases flow rate at the downstream part of the side crest. Results of numerical simulations are exported to Tecplot software, in order to visualize the flow streamlines at different parts of the studied weirs. The weir with oval fillet affects the flow streamlines in three positions: the near bead streamlines of the weir with oval fillet, have less lateral diversion when they reach beneath the overhang of the outlet keys. In other word, streamlines pass this region more smoothly rather than normal PKW. As a result, the fillet decreases the local head loss, when the flow enters the inlet keys. Streamlines of the mid depth level show less contraction at the entrance and middle of the inlet keys. Consequently, lower velocity of the flow along the inlet keys, helps to more evacuation of the flow from side crests. Finally, streamlines release more uniformly from downstream part of the side crest. These phenomena results low submergence level at the middle of the outlet keys. The outlet keys are the brake of nonlinear weirs. By decreasing the submergence level of the outlet keys, flow from the side crests discharge more freely from inlet to the outlet keys.   

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Generally, labyrinth weirs pass more water compared to their equivalent rectangular weirs. Thus, these types of weirs are popular amongst hydraulic and environmental engineers. In this paper, for the first time, a novel artificial intelligence (AI) technique called "outlier robust extreme learning machine (ORELM)" is used to estimate the discharge coefficient of labyrinth weirs. The ORELM method has been proposed in order to overcome the difficulties of the classical ELM in predicting datasets with outliers. In this method, the concept of “sparsity characteristic of outliers” is used. Also, in this study, to verify the results of the numerical models the experimental measurements conducted by Kumar et al. (2011) and Seamons (2014) are employed. The experimental model established by Kumar et al. (2011) is composed of a rectangular channel with a length of 12m, a width of 0.28m and a depth of 0.41m. The weir is made of steel sheets and placed at an 11m distance from rectangular channel inlet. Also, Seamons (2014) experimental model has been set up in a rectangular channel with the length, width and height of 14.6m, 1.2m and 0.9m, respectively. First, the number of the hidden layer neurons initials from 5 and continues to 45 and the most optimal number the hidden layer neurons are taken into account equal to 5. In this study, the Monte Carlo simulations are used for examining the abilities of the numerical models. The main idea of this method is based on solving problems which might be actual in nature using random decision-making. The Monte-Carlo methods are usually implemented for simulating physical and mathematical systems which are not solvable by means of other methods. In this paper, the K-fold cross validation method is employed for validating the results of the numerical models. To this end, the observational data are divided into five equal sets and each time one set of these data is used for testing the numerical model and the rest for training it. This procedure is repeated five times and each test is used exactly once to train and once to test. This method increases the flexibility of the numerical model when dealing with the observational data, and it can be said that the numerical model has the ability to model a greater range of laboratory data. For instance, the maxim value of R2 is obtained for the K=4 case (R2=0.954), while for the K=5 case the values of RMSE and MARE are estimated 0.034 and 4.408, respectively. After that, different activation functions are evaluated in order to detect the most accurate one for the numerical model. Subsequently, six different ORELM models are developed using the parameters affecting the discharge coefficient of labyrinth weirs. Also, the superior model and the most effective input parameters are identified through a sensitivity analysis. For example, the values of R2, RMSRE and NSC for the superior model are calculated 0.943, 5.224 and 0.940, respectively. Furthermore, the ratio of the head above the weir to the weir height (H_T/P) and the ratio of the width of a single cycle to the weir height (w/P) are introduced as the most important input parameters. Also, the results of the ORELM superior model are compared with the artificial intelligence models including the extreme learning machine, artificial neural network and the support vector machine and it is concluded that ORELM has a better performance. Then, an uncertainty analysis is conducted for the ORELM, ELM, ANN and SVM models and it is proved that ORELM has an overestimated performance.

 

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Abstract
In this paper results of experiments on discharge coefficient of rectangular Piano key weirs are presented. Experiments were conducted using two Piano key weirs: one with sloped side walls crest and the other one with horizontal crest. Piano Key weirs with constant value of ratio of length to width were used. The results showed that water level upstream of weir with sloped side walls crest increased by about 11.02 percent. The discharge coefficient of weir with sloped side walls crest increased by about 4.8 percent. The efficiency of weir with sloped side wall crest is increases by about 7.3 percent. New equation for prediction of discharge coefficient of rectangular Piano key weir with sloped side walls crest and horizontal crest was obtained.
 

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Weir is a structure that is made in the body or in supports of a dam to safely discharge the excess volume of water from a reservoir. It is the main factor of safety for dams during floods. A Piano Key Weir (PKWs) is a modified type of labyrinth weir that is designed and built for increasing weir capacity at a specified water head on the weir crest compared to linear weirs. It can provide a specified discharge with a significantly lower upstream water depth. Considering that there is little information about energy loss in PKWs, this article dealt with the experimental study of energy loss in a type-A trapezoidal PKW. The experiments were conducted in a flume made from metal with a length, width, and height of respectively 10, 0.75, and 0.80 m in the hydraulic laboratory of the department of Water and Hydraulic Structures in the Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran. They were performed with weirs with and without steps in their outlet keys at the different flow rates of 30, 40, 50, and 60 L/s. The flow from the upstream tank of 2.05 m length was conducted by a guiding wall to enter the weirs after passing a distance of 1 m. A type-A trapezoidal PKW with 3 keys was utilized. The examined weir had an inlet key width of 0.175 m, outlet key width of 0.051 m, upstream and downstream overhang length of 0.125 m, lateral wall length of 0.5 m, weir height of 0.2 m, weir wall thickness of 0.012 m, and inlet and outlet key slope of 0.53. 3 weir models with different dimensions and number of steps were employed at the outlet keys. The first, second, and third weirs were investigated with 5, 10, and 15 steps, respectively. The PK weir geometry creates a 3D flow field that can be characterized by inclined jet and free fall jet exiting the inlet and outlet keys, respectively. to the downstream and into the outlet keys. The results showed that the energy loss was higher at lower flow rates. The average energy losses were 15.73, 24.93, and 18.52% in the 5-, 10-, and 15-step weirs compared to those without steps, respectively. The discharge coefficients were calculated and compared via two methods. The discharge coefficient calculated with an integral relation was 2.64% higher than that calculated with the general relation for weirs. In addition, this coefficient increased with an increase in the ratio of the weir crest length to its total width. The difference in energy loss measured before the hydraulic jump at a distance of 10 times the weir height was about 3%. The energy loss decreased with an increase in the flow rate and depth of the flow upstream of the weir. The presence of steps at the weir outlet keys had an increasing effect on the energy loss. The highest energy loss (24.93%) was observed in the 10-step weir. Some relations were presented for calculating the amount of energy loss in the type-A trapezoidal stepped PKW, as well as its amount on each step.
 

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In this research, comparison of piano key weir with sharp crested weir and ogee spillway is addressed. The experimentally measured values of discharge of piano key weir were compared with their corresponding computed values for ogee spillway and sharp crested weir.
By using the dimensional analysis technique, dimensionless equation was obtained for discharge coefficient of rectangular piano key weir. Experiments were conducted in a rectangular channel with 10 m length, 0.75 m width and 0.9 m height. Experiments were conducted for various discharges and flow depths. All the experiments were conducted under free flow conditions at weir outlet. The discharge coefficients for the rectangular piano key weir were obtained based on the measured discharges and flow depth. The discharge of ogee spillway and sharp crested weir were estimated by using conventional weir equations.
The variations of discharge versus total upstream head showed almost linear increasing trend of discharge with total head. The plotted data showed a decreasing trend of discharge coefficient with increasing relative total head. The obtained discharge coefficients for the rectangular piano key weir varied between 0.3 and 0.55. The average discharge coefficient for this weir was 0.4.
At H_t/P = 0.28, the discharge through the rectangular piano key is almost 4 times the discharge of the ogee spillway. The average discharge of the piano key weir is about 2.5 times of the ogee spillway and about 3 times that of the sharp crest weir. The energy dissipation of the piano key weir is about 0.3.
According to the results, the piano key weir performs better than the ogee spillway and the sharp crest weir. Therefore, in the circumstances that the design discharge of the dams has increased due to climate changes, the piano key weir is a better alternative to ogee spillway, due to its higher efficiency.
 

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Labyrinth weirs are of the non-linear weirs whose discharge coefficient is higher than similar linear weirs. These weirs have a simple structure. They are mainly made in rectangular, trapezoidal, triangular and semicircular shapes. Investigating the amount of energy loss in these high-efficiency weirs has become very important for engineers in recent years. The experiments were carried out in a flume with a length of 10 meters, a width of 0.6 meters and a height of 0.8 meters. The flow is fed by a pump with an error of 0.01% by three surface tanks and after passing through the flow relaxers into the flume. In this research, four sinusoidal labyrinth weirs were used to check the amount of energy loss. The first spillway has a crown length of 1.3 meters, the second spillway has a crown length of 1.5 meters, the third spillway has a crown length of 1.55 meters, and the fourth spillway has a crown length of 1.6 meters. Also, the first and second weirs have a height of 0.15 meters and the width ratio of the inlet to the outlet is 6.86, and the third and fourth weirs have a height of 0.18 meters and the width ratio of the inlet to the outlet is 7.67. The flow depth in the upstream and downstream of the weir was taken by a point gauge with an error of 1 mm. Weirs are installed at a distance of 5.5 meters from the beginning of the channel. The downstream depth of the spillway was not artificially adjusted by the end valve of the laboratory flume. The weirs are made of wood and wood glue was used for their impermeability. The flow is transferred downstream over the sinusoidal edges of the weir like a curved slide or similar to peak weirs. Also, due to the sinusoidal nature of the weirs, the flow will be transferred downstream faster next to the walls. At the edge of the keys, a local vacuum is created. As the flow rate increases, the available air volume increases. At the downstream of the inlet and outlet keys, a vortex and rotation of the flow is formed, which increases in strength as the flow speed increases. The reason for the formation of vortices is the interference of the falling flow from each sinus. Due to the sinusoidal nature of the flow and the indentations and protrusions in the weir, the flow enters the downstream with a curve and the outflow from each sinus is mixed with the outflow from the other sinus. Also, at the beginning of the outlet keys, a small submerged area is formed, which increases in length and moves downstream as the flow rate increases. In front of the inlet keys, two relatively strong hydraulic jumps are formed, and after that the flow is transferred downstream more calmly. The results were that by increasing the flow rate or increasing the depth of the flow upstream of the weir, the energy loss decreased. Also, the amount of energy loss increases with the effective length of weirs. By increasing the ratio of the width of the input keys to the width of the weir output keys, the amount of energy loss increases. Also, by increasing the ratio of flow depth plus height, such as kinetic energy upstream of the weir to the height of the weir, the amount of energy loss decreases. The amount of energy loss is the highest in the fourth weir and the third weir, respectively. On average, with a 20% increase in the height of the weir, the amount of energy loss increases by 23.2%. Also, the average energy loss in type A, B, C, and D weirs is 42.3, 47.2, 57.9, and 58.6, respectively.