Discharge Coefficient Of Weirs Research Articles

Estimating discharge coefficient of side weirs in trapezoidal and rectangular flumes using outlier robust extreme learning machine

Using the outlier robust extreme learning machine (ORELM) method, the discharge coefficient of side weirs placed on rectangular and trapezoidal canals was simulated for the first time in this study. The parameters governing the discharge coefficient of side weirs including Froude number (Fr), the ratio of the weir length to the main channel length (L/b), the ratio of the flow depth at the upstream of the side weir to the main channel width (y1/b) and the ratio of the crest height of the side weir to the flow depth at the upstream of the side weir (W/y1), the ratio of the weir length to the main channel width (L/y1), and the side wall slope parameter (m) were initially detected. Using the parameters governing, eight different input combinations were defined. By randomly selection approach, 65% of the data were considered to train the ORELM models and the rest of samples were applied to test them. The correlation coefficient, Nash–Sutcliffe efficiency coefficient, and Scatter Index for this model were calculated to be 0.937, 0.869 and 0.092, respectively. The results of sensitivity analysis indicated the ORELM model was more sensitive to the W/y1 and L/b than Fr and y1/b. The results of the ORELM model were also compared with the support vector machine optimized with genetic algorithm (SVM-GA) and extreme learning machine (ELM)) and four multiple linear regression models, with a better performance of the ORELM model. The ORELM models demonstrated a higher precision and correlation with experimental values.

Discharge Coefficient of Rectangular Broad-Crested Weirs in Narrow Channels with High Relative Length of the Threshold

Discharge Coefficient of Rectangular Broad-Crested Weirs in Narrow Channels with High Relative Length of the Threshold

Numerical and experimental modelling of flow at Tyrolean weirs

In this study, a small-scaled Tyrolean weir model was constructed in the laboratory environment and a series of experiments were conducted on it, for two different rack inclinations (θ1 = 18° and θ2 = 25°) and three different bar spacings (e1 = 3 mm, e2 = 6 mm and e3 = 10 mm) for a range of upstream flow discharges. The flow rates passing through the racks and going downstream over the racks were measured. Empirical equations for the discharge coefficient and water capture capacity of the Tyrolean weirs were determined by applying dimensional analysis to the parameters involved in the phenomenon. The related dimensionless parameters were presented with graphs and empirical equations for discharge coefficients were derived, coefficient of determination R2 of equations for θ1 = 18° and θ2 = 25° are found 0.838 and 0.825 respectively. According to results obtained from experimental data, Cd increases as the Froude number ((Fr)e) between bars increases and water capture capacity [(qw)i/(qw)T] of the racks decreases with increasing ((Fr)e). Also, a numerical model of the Tyrolean weir was generated by using Flow-3D software and it was shown that the results of the numerical analysis were very consistent with the physical model results at large bar spacing such as e = 10 mm. As the bar spacing (e) reduces, the success of the numerical model giving consistent results with physical model is decreasing.

Effect of Different Channels on Discharge Coefficient of Labyrinth Weirs

In this study, the effect of channel-bed slope and non-prismatic converging channel on the discharge coefficient of labyrinth weirs is numerically investigated utilizing FLOW-3D model. Numerical simulation results show that modifying the labyrinth weir channel through both methods improves the discharge coefficient. Among the selected bed slopes and converging channel wall, the slope of β=4% and angle of θ=10° yielded the highest discharge coefficient. For a ratio HT/P=0.1, (HT: flow height, P: weir height) the discharge coefficient and discharge rate for bed slope and convergence angle case were 19.22%, 23.9% and 22.28%, 25.91% higher than for a conventional labyrinth weir in prismatic channel, respectively. Simultaneous application of a bed slope and convergence angle significantly increases the discharge coefficient and discharge value case were 28.64% and 30.42% higher than compared to the conventional case. Therefore, changing the bed slope and wall angle of the weir channel increases the discharge coefficient and in this type of weir and these design alterations should be considered in weir design.

Discharge Calculation of Side Weirs with Several Weir Fields Considering the Undisturbed Normal Flow Depth in the Channel

Discharge behavior at side weirs is significantly influenced by the water surface profile along the weir crest. In the past century, different approaches were developed to describe this profile and the associated discharge coefficients. However, the application of these methods to practical problems poses a particular challenge, as a complex three-dimensional funnel is formed due to the discharge reduction, leading to significant uncertainties in determining the relevant flow depth. For this reason, a new approach for the determination of the discharge coefficient of side weirs was developed that refers to the undisturbed normal flow depth in the main channel. Based on a comprehensive parametric study utilizing 3D-numerical simulations, the influence of the weir and channel characteristics on the discharge behavior at the side weir was analyzed. A revised formula for estimating the discharge coefficient for side weirs with multiple weir fields was derived using multiple regression analyses. Validation of the numerical simulations was carried out by applying a physical scale model, showing good agreement between the results.

Experimental investigation of flow characteristics over asymmetric Joukowsky hydrofoil weirs for free and submerged flow

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 h1/L > 0.12 and is greater than that of the ogee weirs for 0.35 < h1/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.

An ISaDE algorithm combined with support vector regression for estimating discharge coefficient of W-planform weirs

AbstractVarious shapes of weirs, such as rectangular, trapezoidal, circular, and triangular plan forms, are used to adjust and measure the flow rate in irrigation networks. The discharge coefficient (Cd) of weirs, as the key hydraulic parameter, involves the combined effects of the geometric and hydraulic parameters. It is used to compute the flow rate over the weirs. For this purpose, a hybrid ISaDE-SVR method is proposed as a hybrid model to estimate the Cd of sharp-crested W-planform weirs. ISaDE is a high-performance algorithm among other optimization algorithms in estimating the nonlinear parameters in different phenomena. The ISaDE algorithm is used to improve the performance of SVR by finding optimal values for the SVR's parameters. To test and validate the proposed model, the experimental datasets of Kumar et al. and Ghodsian were utilized. Six different input scenarios are presented to estimate the Cd. Based on the modeling results, the proposed hybrid method estimates the Cd in terms of H/P, Lw/Wmc, and Lc/Wc. For the superior method, R2, RMSE, MAPE, and δ are obtained as 0.982, 0.006, 0.612, and 0.843, respectively. The amount of improvement in comparison with GMDH, ANFIS and SVR is 3.6%, 1.2% and 1.5% in terms of R2.

Discharge coefficient of broad-crested weirs as a function of the relative weir height for different weir lengths

Broad-crested weirs (BCW) are often used in hydraulic engineering and water management. The most complex factor that affects the discharge capacity of BCW is the discharge coefficient. In Ukrainian engineering practice, the flow rate of BCW is defined as a function of the relative height of the spillway wall, while in the most common European methods – as a function of the relative length of the weir. The experimental dependences of the discharge coefficient of rectangular sharp-edged BCW with vertical inlet and outlet walls with the ratio of the weir length and height d/Р = 2; 4 are obtained. A comparison of the obtained results with the values of the discharge coefficient of the same BCW using the methods of Kumin and Hager indicates that this coefficient depends on both the height of the wall and the length of the weir. The corresponding empirical power law dependences are obtained. At the same values of the relative height of the wall, the discharge coefficient for the weir with the ratio d/Р = 4 is significantly lower comparing the weir with d/Р = 2, that can be explained by the more significant effect of friction resistance for the weir with longer threshold.

A new approach for oblique weir discharge coefficient prediction based on hybrid inclusive multiple model

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

Experimental study and performance comparison on various types of rectangular piano key side weirs at a 120\xb0 section of a 180\xb0 curved channel

Application of side weirs with high effective length is necessary to discharge excessive flows, to control the flow in water conveyance systems, and irrigation and drainage systems. Most of the studies on the side weirs have been conducted on the straight channels and linear weirs. The flow pattern on the outer arc of the curved channels and its suitability for side weir can be used and combined with the piano key weirs. So far, no comparison has been made on rectangular piano key side weirs (RPKSW) at a 120° Section of a 180° Curved Channel. In this study, an experimental study was performed on A-, B-, C-, and D-type RPKSW at a bend angle of 120 degrees. The results showed that the specific energy at two ends of the RPKSWs was the same, with a slight difference of 3.4% for A-Type, 1.3% for B-Type, 1.1% for C-Type, and 1.8% for D-Type weirs. The discharge coefficients of the studied weirs were also investigated, and it was concluded that B-Type weir has better performance than other weirs. On average, the discharge coefficient of B-Type weir was 9.9%, 21.2%, and 24.1% higher than that of A-Type, C-Type, and D-Type weir, respectively. It was shown that the ratio of P/h1 is the main parameter affecting the weir discharge coefficient. Finally, an empirical equation was proposed for each weir. The proposed equation has MAE = 0.028 for A-Type weir, MAE = 0.041 for B-Type weir, MAE = 0.049 for C-Type weir, and MAE = 0.053 for D-Type weir.

Laboratory investigation of the discharge coefficient of triangular labyrinth weirs with and without slots and comparing them with piano key weirs*

AbstractWith an increase of the length of a crest in a given width, labyrinth weirs lead to an increase in flow transition capacity over the weir. This study was performed on a laboratory flume with a length of 12.5 m, width of 0.3 m and a height of 0.4 m, using triangular labyrinth weirs (with and without slots), each having single‐ and two‐cycle models. First, their hydraulic performance was examined, and then it was compared with that of a piano key weir (single‐cycle, two‐cycle). The results showed that the increase in crest length through a slot in single‐ and two‐cycle weirs cannot be an effective factor. The presence of a slot in single‐ and two‐cycle triangular weirs led to a decrease in the discharge coefficient of these weirs up to 35 and 33% respectively, compared to weirs without any slot. This is due to energy loss, local submergence and flow interference in the nose slot even at low flows. However, the flow's index weir (triangular weir slot, one slot) compared to single‐ and two‐cycle piano key weirs dropped by 40 and 26% respectively.

A Proposed Novel Hybrid Intelligent Model Based on ANFIS Integrated with Firefly Algorithm for Forecasting Discharge Coefficient of Side Weirs on Converging Canals*

AbstractSide weirs are widely used to measure and control flows passing through main canals. In this study, a hybrid model is developed to approximate the discharge coefficient of side weirs located on converging canals for the first time, meaning that the adaptive neuro‐fuzzy inference system (ANFIS) network is optimized by means of the firefly algorithm. After that, six ANFIS and adaptive neuro‐fuzzy inference system‐firefly algorithm (ANFIS‐FA) models are introduced using input parameters. In addition, in this study, Monte Carlo simulation is employed to study the modelling accuracy. Furthermore, the k‐fold cross‐validation approach is implemented to validate the modelling results. Analysing the modelled results demonstrates that the hybrid models are more accurate than the ANFIS ones. The superior model simulates the discharge coefficient values with reasonable accuracy. For example, the values of the determination coefficient (R2), the mean absolute error (MAE) and the root mean square error (RMSE) for the superior model are calculated as 0.993, 0.011 and 0.015, respectively. Also, about 98% of the superior model results have errors less than 12%. According to the uncertainty analysis results, the superior model has an overestimated performance. A sensitivity analysis indicates that the flow Froude number at the side weir downstream is the most effective input parameter. © 2020 John Wiley &amp; Sons, Ltd.

Experimental Investigation of Arched Sharp-Crested Weir Flow and Comparing it with Rectangular Weir

The hydraulic behavior of the arched sharp-crested weirs is investigated and compared with rectangular weirs in this research. For this purpose, a laboratory study was made on a physical model, including weirs with four different arc lengths each with five different heights. Experiments were carried out in free flow condition and in both aerated and non-aerated cases of weirs. Laboratory data were discharge rate and water head amount on weir. The water head on weir has been read over the course of various discharge flows over a range of about 3–140 l/s. Test results proved that the arched weir discharge coefficient, while seriously dependent on the $$\frac{H}{P}$$ ratio, is also a function of the weir arc length. The variations of this coefficient with respect to $$\frac{H}{P}$$ ratio are nonlinear and different from rectangular weir one. It will be reduced and attain an almost constant amount by increasing the ratio. Experimental results show that the circle discharge coefficient amount is bigger than rectangular one in $$\frac{H}{P}$$ values less than 0.2 and it is smaller than one in $$\frac{H}{P}$$ ratio more than 1.2. Moreover, arched weir discharge value is always more than the rectangular weir in the same status. In the range of present experiments, increments of the arched weir discharge relative to the rectangular vary from 10 up to 80%. It depends on the height and length of the weir crest.

Numerical modelling of contracted sharp‐crested weirs and combined weir and gate systems

AbstractDischarge measurement and control structures are widely employed in hydraulic engineering applications. The objective of this study is to numerically investigate the modelling of two different structures, namely sharp‐crested weirs as Problem 1 and combined weir and gate systems as Problem 2. The research methodology herein is based on the comparison of results of numerical simulations with experimental data for both problems separately. For the purpose of performing numerical simulations, the Reynolds‐averaged Navier–Stokes (RANS) equations are solved by finite volume formulation using commercially available Flow‐3D software. Assessment of empirical data and numerical findings for both problems reveals that discharge rates agree reasonably well. In addition, using the capabilities of numerical modelling, weir and gate discharge coefficients in the combined system are calculated separately which were not easy to obtain in experimental studies. It is seen that gate and weir discharge coefficients of the combined system are different and higher than the corresponding coefficients of the individual systems. © 2020 John Wiley &amp; Sons, Ltd.

An experimental study of the effects of the parapet walls geometry on the discharge coefficient of trapezoidal piano key weirs

Parapet walls on the crown of piano key weirs (PKW) are employed in the channels to regulate or increase water levels of the upstream. They are also used in the reservoirs to increase water storage. Most recent surveys concerning discharge coefficient and parapet walls have been conducted on the rectangular piano key weirs (RPKW) while not many of them devoted to trapezoidal piano key weirs (TPKW). Also, the effects of its parapet wall and crest shape are rarely investigated in this regard. The aim of this research was to study the impacts of height (R), installation arrangements (S), and crest shape of parapet walls (flat, triangular, and semicircular) on changes of the upstream water level and discharge coefficient of TPKW. The weir height (P) was 15 cm. The parapet walls were installed on the crest of weir with three different arrangements: S1 (on the crest overall), S2 (on the sidewalls and inlet key), and S3 (on the sidewalls). The results indicated that the influence of installation arrangement on changes of water level increased with the growth of parapet walls height. In the case of a flat parapet walls, maximum and minimum increase rates of total head were recorded for S1 and S3 arrangements, respectively. There was also a direct relationship between discharge coefficient (C) and the heights of parapet walls in a constant water level at upstream. When installing flat parapet walls with R/P = 0.3, the value of C for S2 exceeded those for S1 and S3.

A NEW NON‐TUNED SELF‐ADAPTIVE MACHINE‐LEARNING APPROACH FOR SIMULATING THE DISCHARGE COEFFICIENT OF LABYRINTH WEIRS

AbstractIn this study, the labyrinth weir discharge coefficient was simulated using the self‐adaptive extreme learning machine (SAELM) artificial intelligence model in two cases: normal orientation labyrinth weirs (NLWs) and inverted orientation labyrinth weirs (ILWs). First, the most optimized neuron of the hidden layer was computed. The number of hidden layer neurons was calculated as 30. Also, by analysing the results of different activation functions, it was concluded that the sigmoid activation function has higher accuracy than the others. Next, the superior model was identified by conducting a sensitivity analysis. The model approximated the discharge coefficient of labyrinth weirs with reasonable accuracy. For example, the R2, scatter index and Nash–Sutcliffe efficiency coefficient for the best model were estimated as 0.966, 0.034 and 0.964, respectively. In addition, the ratio of the total head above the weir to the height of the weir crest (HT/P) and the ratio of length of apex geometry to width of a single cycle (A/w) were identified as the most effective parameters. Furthermore, the uncertainty analysis results indicated that the superior model had an overestimated performance. Then, a relationship was proposed in terms of all input variables for the superior model. © 2020 John Wiley &amp; Sons, Ltd.

Experimental and numerical analysis of flow hydraulics in triangular and rectangular piano key weirs

ABSTRACT Piano key weir is a new type of spillways designed to improve the discharge capacity of dams. Generally, increasing the upstream hydraulic load in piano key weirs results in reduced discharge capacity of the weir. Accordingly, the present study investigated the effects of triangular notch on the discharge coefficient of piano key weirs. The 3D flow field over the piano key weirs was simulated in FLOW-3D software in order to study the flow hydraulics and compare the discharge rates, and the effect of each model on the flow field over the weirs and discharge coefficient was investigated. The results suggested that data of the numerical model were appropriately consistent with that of the laboratory model. According to the results, the discharge coefficient of the triangular piano key weirs was 25% higher than that of the rectangular piano key weirs. It was also observed that changing the notch shape of the piano key weir increased the discharge coefficient of the piano key weir by 36% and 13% for the heights of 5 cm of 7.5 cm, respectively.

Simulation of discharge coefficient of side weirs placed on convergent canals using modern self-adaptive extreme learning machine

Side weirs are broadly used in irrigation channels, drainage systems and sewage disposal canals for controlling and adjusting the flow in main channels. In this study, a new artificial intelligence model entitled “self-adaptive extreme learning machine” (SAELM) is developed for simulating the discharge coefficient of side weirs located upon rectangular channels. Also, the Monte Carlo simulations are implemented for assessing the abilities of the numerical models. It should be noted that the k-fold cross-validation approach is used for validating the results obtained from the numerical models. Based on the parameters affecting the discharge coefficient, six artificial intelligence models are defined. The examination of the numerical models exhibits that such models simulate the discharge coefficient valued with acceptable accuracy. For instance, mean absolute error and root mean square error for the superior model are computed 0.022 and 0.027, respectively. The best SAELM model predicts the discharge coefficient values in terms of Froude number (Fd), ratio of the side weir height to the downstream depth (w/hd), ratio of the channel width at downstream to the downstream depth (bd/hd) and ratio of the side weir length to the downstream depth (L/hd). Based on the sensitivity analysis results, the Froude number of the side weir downstream is identified as the most influencing input parameter. Lastly, a matrix is presented to estimate the discharge coefficient of side weirs on convergent channels.

Experimental study and modelling discharge coefficient of trapezoidal and rectangular piano key weirs

Crest length is an important parameter in influencing the discharge handling capacity of a weir. Nonlinear weirs with longer crests are cost effective alternatives for those existing dam structures which are more susceptible to failure due to loss of storage capacity by reservoir silting problem, and insufficiency of the structure in evacuating the updated flow due to the limited space. Piano key weir is a type of nonlinear weir designed in the form of piano keys, over-hanged from both the upstream and the downstream with sloping floors founded on a base or footprint. These weirs can be easily placed over gravity dams due to smaller footprint than labyrinth weirs. The present study’s focus is on the comparative analysis of identical configurations of trapezoidal and rectangular piano key (PK) weirs. The importance of (crest length to width) L/W ratio and weir height (P) in affecting the discharge efficiency of both types of PK weirs is investigated in the experimental study. Furthermore, soft computing approaches are applied to the current data set obtained from both types of weirs by considering discharge coefficient (C_{text{d}}) as a function of dimensionless geometric variables of PK weirs. The modelling performance of random forest regression and M5 tree approach is tested in order to estimate the values of discharge coefficient. The results conclude higher predictive accuracy of random forest model over M5 tree model.

Prognostication of discharge coefficient of labyrinth weir using outlier robust extreme learning machine

In this paper, for the first time, a robust artificial intelligence (AI) technique called “outlier robust extreme learning machine (ORELM)” is used to estimate the discharge coefficient of labyrinth weirs. At the beginning, the number of the hidden layer neurons initials from 5 and continues to 45 and the most optimal number of the hidden layer neurons are taken into account equal to 5. Then, the numerical model is verified by the k-fold cross-validation approach in which k is considered equal to 5. After that, different activation functions are evaluated 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 (HT/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 the ORELM has an overestimated performance. Eventually, a practical formula is presented to engineers without knowledge of artificial intelligence for approximating the discharge coefficient of labyrinth weirs. Additionally, a partial derivative sensitivity analysis is carried out for this equation.