Rectangular Sharp-crested Weir Research Articles

Discharge formula based on brink depth over sharp-crested weirs

Abstract Weirs are among the most essential hydraulic structures for measuring water discharge in open channels. The prediction of water discharge over weirs should be as precise and straightforward measured as feasible. The experimental investigation of flow prediction over varied heights of a conventional rectangular sharp-crested weir was conducted in the present work. The investigation evaluated five ratios of weir height to length, P/b, of 0.33, 0.4, 0.47, 0.53, and 0.6, different water discharges, Q, of up to 17.25 L/s, and different bed slopes, S, between 0.001 and 0.01. The experiment's findings reveal that a change in the bed slope has no significant effect on the brink depth, hb, for a constant water discharge. However, it influences the head over the weir, h, which is usually measured upstream of the weir location and used to predict water discharge. A simple, accurate formula was developed for predicting water discharge over rectangular sharp-crested weirs depending on the brink depth with mean absolute percent error (MAPE) and root-mean-square error (RMSE) of 1.714% and 0.229, respectively. In addition to having a simple form, the developed formula performs well, is unaffected by the bed slope, and applies to a wide range of h/P values, from 0.158 to 0.945.

A comprehensive experimental investigation on discharge formulae of free flow over fully contracted rectangular sharp-crested weirs

In this study, laboratory experiments were conducted to investigate the discharge characteristics of free flow over rectangular sharp-crested weirs under the situation of large discharges and high water heads. By adding the weir plates with contraction ratios which were not considered in the literature, a new division for the rectangular sharp-crested weirs was proposed. The performances of the available discharge coefficient equations from the literature were evaluated and improved. It was found that the water head has significant effect on the accuracy of the proposed discharge coefficient equations. The discharge coefficient is suitable to be described by the Reynolds number at low heads and the contraction ratio at high heads, this is determined by the flow characteristics of the rectangular sharp-crested weir. The work presented in this paper would be useful to enrich and develop the research on the flow discharge of rectangular sharp-crested weirs.

Investigating the process of changing the discharge coefficient of the flow passing through the combined structure of rectangular sharp-crested weir with multiple-gates

To investigate the effect of the number and dimensions of the gates-weir structure, 117 experimental tests were carried out at different flow rates, numbers and dimensions of square gates. The experiments were carried out in a laboratory flume with a length of 12 m. The results showed that with the increase in the number and dimensions of the gates in combined weir-gate structure, the combined discharge coefficient was increased. These changes are such that the combined discharge coefficient is increased by 3.8% with the increase of each gate. The results showed that the lowest and the highest increase in the flow coefficient was observed in the comparison between the single gate and the 5-gate condition compared to the no-gate condition by 16% and 18%, respectively. In the following, a relationship was presented to determine the combined discharge coefficient with RMSE = 0.001.

Flow regimes of submerged rectangular sharp-crested weirs in sand bed channel

Flow regimes of submerged rectangular sharp-crested weirs in sand bed channel

Hydraulics of flow over full-cycle cosine and rectangular sharp-crested weirs

Laboratory experiments were carried out to investigate the hydraulic characteristics of full-cycle cosine and rectangular sharp-crested weirs in free flow condition. The head–discharge relationships of full-cycle cosine weirs were determined theoretically and the discharge coefficients were correlated with weir geometry for both rigid and erodible bed conditions. The proposed model showed higher discharge coefficients in full-cycle cosine weirs in comparison with rectangular sharp-crested weirs. The three-dimensional velocity profiles of full-cycle cosine and rectangular weirs were measured by an acoustic Doppler velocimeter probe. The effects of weir geometry on mean flow and local erosion upstream of the weirs were studied for two sediment sizes of 0.7 mm and 1.2 mm. The time-averaged velocity profiles exhibited strong three-dimensional flow in full-cycle cosine weirs. The strength of the upper eddy in the crest location of full-cycle cosine weirs decreased by increasing the weir gap opening and the jet stream deflected upward due to uneven eddy sizes. The maximum streamwise velocity of cosine weirs increased by four times the average velocity at the crest level of the weir and the transverse velocity profiles captured strong vortices in the vertical plane closest to the weir. The effect of weir gap opening of full-cycle cosine weirs on the total scour volume was studied for two sediment sizes. It was found that the scour volume in the upstream region of cosine weirs was higher than the scour volume formed upstream of a rectangular weir with the same opening.

Experimental study of discharge formulas for rectangular sharp-crested weirs under free flow condition

Laboratory experiments were carried out to investigate the discharge characteristics of rectangular sharp-crested weirs under free flow condition. The performances of available discharge formulas have been evaluated by using the experimental data sets of present and previous studies. Error statistics of our experimental data indicate that the recent stage-discharge relationships show satisfactory performances. Discharge formula in terms of weir Reynolds number proposed by Vatankhah gives the highest accuracy among the existing slit weir equations, with E±4=100.00% (i.e. percent error less than or equal to ±4) and a mean absolute error |E|m=0.88%. The full-range discharge equation presented by Bijankhan and Mahdavi Mazdeh shows the highest accuracy among the relationships in terms of weir contraction ratio, with E±4=100.00%, |E|m=0.91% for slit weirs and, E±4=94.64%, |E|m=1.60% for partially contracted weirs, respectively. The weir velocity formulae suggested by Gharahjeh et al. exhibit the relatively better performance, with E±4=98.41%, |E|m=1.34% for slit weirs and, E±4=91.07%, |E|m=1.91% for contracted weirs, respectively. Statistical results of this study confirm the weir velocity approach presented by Aydin et al. and show that, the weir velocity is a predominant quantity for rectangular sharp-crested weirs, unique characteristics of the weir velocity curves make it more suitable for expressing the discharges. Moreover, it is important to point out that the performance of weir velocity formulae can be further improved.

An Extra Tree Regression Model for Discharge Coefficient Prediction: Novel, Practical Applications in the Hydraulic Sector and Future Research Directions

Despite modern advances used to estimate the discharge coefficient ( C d ), it is still a major challenge for hydraulic engineers to accurately determine C d for side weirs. In this study, extra tree regression (ETR) was used to predict the C d of rectangular sharp-crested side weirs depending on hydraulic and geometrical parameters. The prediction capacity of the ETR model was validated with two predictive models, namely, extreme learning machine (ELM) and random forest (RF). The quantitative assessment revealed that the ETR model achieved the highest accuracy in the predictions compared to other applied models, and also, it exhibited excellent agreement between measured and predicted C d (correlation coefficient is 0.9603). Moreover, the ETR achieved 6.73% and 22.96% higher prediction accuracy in terms of root mean square error in comparison to ELM and RF, respectively. Furthermore, the performed sensitivity analysis shows that the geometrical parameter such as b/B has the most influence on C d . Overall, the proposed model (ETR) is found to be a suitable, practical, and qualified computer-aid technology for C d modeling that may contribute to enhance the basic knowledge of hydraulic considerations.

Flow and Energy Loss Downstream of Rectangular Sharp-Crested Weirs for Free and Submerged Flows

Abstract This work presents an analytical study of the flow and energy loss immediately downstream of rectangular sharp-crested weirs for free and submerged flows, using the theory of plane turbulent jets and the analysis of some relevant studies. The flow regimes downstream of the sharp-crested weir is characterized as the impinging jet and surface flow regimes. Based on the flow characteristics and the downstream tailwater depths, each flow regime is further classified, and the relative energy loss equation is developed. It is found that significant energy loss occurs for the regime of supercritical flow and the upper stage of impinging jet flow. The energy loss for the submerged flow regime is minimal.

Discharge prediction for rectangular sharp-crested weirs by machine learning techniques

The stage-discharge relationship of a weir is essential for posteriori calculations of flow discharges. Conventionally, it is determined by regression methods, which is time-consuming and may subject to limited prediction accuracy. To provide a better estimate, the machine learning models, artificial neural network (ANN), support vector machine (SVM) and extreme learning machine (ELM), are assessed for the prediction of discharges of rectangular sharp-crested weirs. A large number of experimental data sets are adopted to develop and calibrate these models. Different input scenarios and data management strategies are employed to optimize the models, for which performance is evaluated in the light of statistical criteria. The results show that all three models are capable of predicting the discharge coefficient with high accuracy, but the SVM exhibits somewhat better performance. Its maximum and mean relative error are respectively 5.44 and 0.99%, and 99% of the predicted data show an error below 5%. The coefficient of determination and root mean square error are 0.95 and 0.01, respectively. The model sensitivity is examined, indicative of the dominant roles of weir Reynolds number and contraction ratio in discharge estimation. The existing empirical formulas are assessed and compared against the machine learning models. It is found that the relationship proposed by Vatankhah exhibits the highest accuracy. However, it is still less accurate than the machine learning approaches. The study is intended to provide reference for discharge determination of overflow structures including spillways.

A Study of The Turbulent Flows behind A Rectangular Sharp Crested Weir in Open Channel Using Laser Doppler Velocimetry (Dept.C)

This paper describes the experimental investigation using laser Doppler velocimetry) (LDV) in the downstream of .be rectangular sharp crested weir in a horizontal rectangular channel of constant width. The study was carried out for flows on smooth and rough weir. For precise and accurate measurements of mean and fluctuating a ting flow characteristics such as streamwise and vertical turbulence intensity components and streamwise and vertical mean velocity components. The depthwise measurements were carried out for different heights of the weir along to e centerline at different cross sections downstream of weir in the wake region . The results show that, the measured values of turbulence intensities are found to have high level of turbulence in the Dear wake region but are low in the far wake region. The turbulence intensities depict the occurrence of a constant turbulence close to the wall in the far wake region. The roughness was found to increase the turbulence. Also, it can be seen that with increasing weir height, the turbulence intensities are Increased.

Three-Dimensional Simulation of Flow Over Sharp-Crested Weirs Using Volume of Fluid Method

Abstract In sharp crested weirs, significant changes occur in the hydraulic characteristics of the flow past the weirs with different geometry. A detailed investigation and better understanding of hydraulic behavior will help practically to choose an appropriate geometry for weir. The purpose of this research is simulate the flow over sharp crested weir and investigate the effect of geometric shapes of sharp crested weirs on hydraulic characteristics of the flow such as pressure, velocity, water level profiles and discharge coefficients. Thus the limitation and usage range of sharp crested weirs are clarified. In this research OpenFOAM open source 3D software with RNG K-ε turbulence model and Volume of Fluid method (VOF) was used to analyze the hydraulic flow passing through sharp crested weir. The correlation coefficient for flow Surface profiles and discharge coefficients among numerical and experimental data is obtained 0.96 for different discharge rates. In the present research, discharge coefficients for rectangular weirs with compression coefficient 0%, trapezoidal and triangular weirs are determined 1.20, 0.68 and 0.51 respectively using discharge rate of 0.05183m3/s. The maximum discharge coefficient is obtained for rectangular sharp crested weir while the triangular sharp crested weir has minimum discharge coefficient.

Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs

Currently, discharges passing measurement devices and structures in unsteady flow conditions are determined based on relationships developed for steady flow condition due to lack of sufficient data. In this study, the operation of triangular and rectangular sharp-crested weirs in unsteady flow conditions was experimentally investigated. The compiled data indicated the presence of looped rating curves, but with transposition of the rising and falling limbs compared to that commonly observed in stream gauge ratings. The presence of such looped rating curves was justified, and the validity of the steady rating curve relationships, which are presently being applied to unsteady flow conditions, was questioned. Accordingly, relationships for evaluating unsteady discharge passing different rectangular and triangular sharp-crested weirs were presented. The proposed formulas considerably improve the discharge measurements accuracy in unsteady flow conditions and could be incorporated in hydrodynamic models.

Aplikasi Persamaan Rehbock, Kinsvater – Carter, Dan Persamaan Umum Pada Bangunan Ukur Segi Empat Skala Laboratorium

The rectangular sharp-crested weir often finds in irrigation open channels. The function of the rectangular sharp-crested weir measures and divides the water flow to be distributed to agricultural lands. The Rehbock equation, the Kinsvater-Carter equation, and the General equation are used to approach the discharge. On a laboratory scale, the measurement of the discharge using a small rectangular sharp-crested weir was used for experiments and simulations. Because of using The Rehbock equation, The Kinsvater-Carter equation, and The General equation for a field discharge measurements, it is necessary to research to find out the accuracy of the Rehbock Equation, the Kinsvater-Carter equation and the General equation in the laboratory scale. The research data included the dimensions of rectangular weirs, the height of the water on the rectangular sharp-crested weir, the width of the channel on the hydraulic bench and the actual discharge. Data collection of the height of water on the rectangular sharp-crested weir and the actual discharge was carried out 5 times the measurements with different discharges. These data were analyzed using the Rehbock equation, the Kinsvater-Carter equation, and the General equation. The discharge of the analysis results was compared with the actual discharge to find out the value of the calibration coefficient. The experimental results show that the Kinsvater-Carter equation and General equation can be applied for discharge measurements on the laboratory scale. The calibration coefficient for the Kinsvater-charter equation was 0.89 and the calibration coefficient for the general equation was 0.94.

Mean velocity and turbulent characteristics of flow over half-cycle cosine sharp-crested weirs

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.

Energy harvesting from water flow in open channel with macro fiber composite

Fluid-induced vibrational energy harvesting usually concerns small-scale wind energy extraction. A few efforts have been made into energy harnessing from low-velocity water flows. In this study, low-speed galloping and vortex induced vibration (VIV) are investigated for energy harvesting in an open channel via the macro fiber composite glued on the surface of a cantilever beam. A cylindrical or triangular-prism bluff body is attached at the free tip of the beam and fully immersed in the water. Beam’s deflection is perpendicular to the fluid flow. The flowrate of the water channel is measured by a built-in rectangular sharp-crested weir, and the average flow velocity is controlled by the inlet valve and weir plate. The fluid-structure interaction and electromechanical coupling at different flow velocities and load resistances are analyzed. At small flow velocities, the cylindrical bluff body exhibits better performance than the triangular-prism bluff body since it has been shown in previous work [So et al., J. Fluid Struct. 24, 481–495 (2008) and Daniels et al., J. Wind Eng. Ind. Aerod. 153, 13–25 (2016)] that for the same turbulence intensity the cylinder under VIV performs better than the triangular prism. As the flow velocity increases, the power of the triangular-prism case harvested from the interaction of low-speed galloping and VIV overtakes the power of the cylindrical case converted from the VIV motion that is usually smaller than the cylinder diameter. One dominant vibration frequency is noticed and associated with lock-in or wake capture, which increases with the flow velocity owing to the decreasing added mass. High efficient energy harvesting from the low-velocity water flow is realized via the integration of galloping and VIV.

Numerical Investigation of Geometric Parameters Effect of the Labyrinth Weir on the Discharge Coefficient

Weirs, as overflow structures, are extensively applied for the measurement of flow, its diversion, and control in the open canals. Labyrinth weir as a result of more effective length than conventional weirs allows passing more discharge in narrow canals. Determination of the design criteria for the practical application of these weirs needs more examination. Weir angle and its position relative to the flow direction are the most effective parameters on the discharge coefficient. In this article, Fluent software was applied as a virtual laboratory, and extensive experiments were carried out to survey the effect of geometry on the labyrinth weir discharge coefficient. The variables were the height of weir, the angle of the weir, and the discharge. The discharge coefficients acquired from these experiments were then compared with the corresponding values obtained from the usual rectangular sharp-crested weir experiments. Comparison of the results indicated that in all cases with different vertex angle, flow discharge coefficients are in a satisfactory range for relative effective head less than 0.3. The discharge coefficient is reduced for relative effective head more than 0.3 due to the collision of water napes. It revealed that the higher the weir, the more discharge capacity. As a result, the labyrinth weirs have a better performance in comparison with the common sharp-crested.

Lateral flow through the sharp crested side rectangular weirs in open channels

A side rectangular weir is a flow diversion structure provided in the side wall of a channel to divert water from main channel to a branch channel. They are widely used in hydraulics, environmental and irrigation engineering for controlling and directing flow of water in irrigation–drainage systems, waste water channels, drainage canal systems, diverting excess water into relief channels for flood-protection works, and as storm overflows from urban sewage systems. The present study is aimed at to compile the past observations on coefficient of discharge for side rectangular sharp crested weir, supplement them with new experimental results and reanalysing resulting data bases with a view towards seeing if better prediction are possible. Therefore, a new model for determination of coefficient of discharge of side rectangular sharp crested weir is developed. It is observed that approach Froude number is an important parameter for coefficient of discharge. The ratio of the crest height of side weir to length of the side weir, ratio of width of the main cannel to length of side weir and ratio of the upstream depth in the channel to length of side weir also affect the coefficient of discharge. The performance of the present model is based on the coefficient of correlation of the linear regression line between predicted values from the present model and desired output (R), mean absolute percentage error (MAPE), average percentage error (APE), root means square error (RMSE) etc. The qualitative performance of the present predictor indicates that it has highest R (0.865) and lowest MAPE (4.8936), RMSE (0.0337), APE (−0.346) as compared to other existing predictors. Flow profile and flow pattern are also observed in the vicinity of side weir in the main channel.

River safe yield with the constraint of a contracted rectangular weir for surface water supply

Aydin et al. introduced the weir velocity concept in 2011 for discharge measurement in contracted rectangular sharp-crested weirs. Gharahjeh et al. further reinforced this formula in 2015 to allow discharge to be computed using only weir velocity and crest width. These newly introduced expressions are tested and demonstrated to determine surface water yield of Tapah River in Sarawak. Aydin and Gharahjeh's formula is found to perform similarly to the improved discharge coefficient developed by French in 1986, but is simpler and easier to use. Exploring Aydin and Gharahjeh's formula through theoretical, experimental, and field approaches, it has been found that the formula performs well in a controlled environment. Discharge computations based on field data were determined to have been formerly underestimated, with the reason as yet undetermined.

Water Surface Characteristics of Submerged Rectangular Sharp-Crested Weirs

AbstractLaboratory 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...

Elementary discharge coefficient of a triangular–rectangular sharp-crested side weir in subcritical flow

ABSTRACTSide weirs or lateral weirs are widely employed to divert flows from rivers, channels, sewers and reservoirs or to divide flows between components of water treatment systems. The side weir is a fixed structure installed at one side of a channel for water level control in water treatment plants and irrigation and drainage systems. Hydraulic characteristics of a compound sharp-crested triangular–rectangular side weir under subcritical flow were studied in this paper. The concept of the elementary discharge coefficient that is related to the head to weir height ratio was used to determine the flow through the side weir. The advantage of this method is to calculate the channel water surface profile along the weir. Generalized equations for an elementary discharge coefficient for compound triangular–rectangular side weirs were proposed. Experimental results show the accuracy of the proposed equations.