Flow over trapezoidal side weir

In this paper, the hydraulic characteristics of a sharp crested trapezoidal side weir have been experimentally and theoretically investigated. It was found that the DeMarchi coefficient of discharge for a sharp crested trapezoidal side weir in subcritical flow is related to the main channel Froude number, the side slope of weir, ratio of weir height to upstream depth of flow and ratio of weir length to upstream depth of flow. Suitable equations for the discharge coefficient are also obtained.     

Discharge coefficient for an inclined side weir crest using a constant energy approach

In this paper, the inclined side weir discharge coefficient was studied using a side weir with three different crest angles (θ=4°,8°,12°) fixed either against and in the flow direction, and the results are compared with those from a horizontal side weir crest (θ=0°). In total there were seven models.The results show that the De Marchi assumption of constant energy for all side weir crested angles is acceptable, and thus that the calculated weir discharge value can therefore be undertaken.An equation for the discharge coefficient was obtained for an inclined side weir, so the value of C_d for crest angle θ=12° increased by 13.6% with respect to the value for θ=8°, by 29% with respect to that for θ=4°, and by 39% with respect to that for the horizontal case (θ=0°), for a crest inclined against the flow direction, while when the crest was inclined in the flow direction all those values exceed, to 14.5%, 31.0%, and 40.7%, respectively. This means that the discharge increases with increasing side weir crest angle, so when we want uniformity in the flow direction and exceed discharge we need to make the side weir crest incline against the flow direction while when we want furthermore discharge we need to make the side weir crest incline in the flow direction.     

Flow characteristics over asymmetric triangular labyrinth side weirs

Side weir is placed at the channel bank as a head regulator or a diversion device. Flow over a side weir has been the subject of many research studies considering its three dimensional and complicated characteristics. However, the labyrinth side weirs warrant further research due to their higher efficiency compared to linear side weirs. In this paper, subcritical flow characteristics and discharge coefficient for both symmetric and asymmetric triangular labyrinth side weirs were studied experimentally. The results show that asymmetric labyrinth side weirs have higher discharge coefficient compared to symmetric labyrinth side weirs; since a larger portion of the crest is orthogonal to the flow. Using the present laboratory data, general equations were proposed for the estimation of discharge coefficient of both symmetric and asymmetric triangular labyrinth side weirs. The results of this study can be useful to design side weirs with high hydraulic performance.     

Hydraulic characteristics of a new weir entitled of quarter-circular crested weir

Weirs are used for flow measurement, flood control in reservoirs and water level control in irrigation systems. In this study, a new weir entitled of quarter-circular crested weir is investigated. This weir is geometrically consisted of a quarter-circular crest of radius R, upstream slope α and vertical downstream face. The downstream face of the weir must be ventilated. Discharge coefficient, crest section velocity and pressure profiles, pressure distribution on the crest surface and upper and lower nappe profiles of flow over the quarter-circular crested weir were experimentally investigated. Results indicated that discharge coefficient of the weir is a constant value and equals to 1.261. In the range of H/R<1.5, it is more than the discharge coefficient of circular crested weir. The lower nappe profile of free jet over the weir can also be considered as the ogee shape of the proposed weir.     

Estimating the uncertainty of discharge coefficient predicted for oblique side weir using Monte Carlo method

Side weir is a hydraulic structure, which is used in irrigation systems to divert some water from main to side channel. It is installed at the entrance of the side channel to control and measure passing water into the side channel. Many studies provided side weir water surface profile and coefficient of discharge to measure water discharge diverted into the side channel. These studies dealt with different side weir shapes (rectangular, trapezoidal, triangular and circular), which were installed perpendicular to the flow direction. Recently, some studies dealt with skew side weir, but these studies still need to more investigation. Here we report to investigate oblique side weir theoretically using statistical method to supported other studies in this case. Measurement uncertainty discharge coefficient C_d was obtained by two methods: analytical according to the ‘Guide to the expression of uncertainty in measurement’ and the Monte Carlo method. The results indicate that all experimental results are consistent with the analytical results. The relative expanded uncertainty of the discharge coefficient C_d does not exceed 2%.     

Discharge equation for the gabion weir under through flow condition

A gabion weir is considered to be more environmentally friendly as compared to an impermeable weir, as its permeability allows substances and aquatic life to pass through it. Also, gabion weirs offer an alternative design with low afflux that could be adopted for flash flood mitigation. In the present study, a series of laboratory experiments were performed on flow through gabion weir of various sizes and for varying boulder sizes and discharges. Collected data were used to check the accuracy of the existing relationships between hydraulic gradient and flow velocity for highly porous material like gabion filled with boulders. It is found that Ergun's equation predicts the hydraulic gradient more accurately than the other available equation. Ergun's equation is extended to calculate the flow through the gabion weir. The derived discharge equation for flow through gabion weir was validated with the collected data. A qualitative performance of the present model indicates that it has the highest coefficient of correlation (R = 0.956) and the lowest MAPE (16.902), RMSE (0.002), AAD (15.52). It was found that the derived equation computes discharge within a maximum of ±10% error for almost all data sets, which can be considered satisfactory from practical consideration. Sensitivity analysis reveals that the discharge through the gabion weir is more sensitive to the boulders diameter and upstream depth as compared to the downstream depth of the gabion weir.     

A flow field characterization in a circular channel along a side weir

Side weirs have been used for centuries in urban drainage and flood control for their ability to divert high incoming flow rates. The flow along a side weir may be studied by means of different approaches. However, although the question of side weir has been debating for many decades, there are few studies on the local hydraulic characteristics of the flow along these structures in circular channels.An experimental study of the flow field in a circular channel along a side weir using a commercial TSI Particle Image Velocimetry (PIV) system is shown in this paper. Weakly supercritical flows running into different geometric configurations of the weir were investigated, with Froude numbers varying from 1.1 to 1.6. Free surface profiles have been obtained by an image processing technique. An empirical equation has been proposed for their representation. Longitudinal velocity profiles along the side weir can be well predicted by an entropic approach. Local outflow along the side weir may be represented by an asymmetric curve. The peak outflow generally occurs between the 30% and the 50% of the weir length. The elementary discharge coefficient significantly increases from upstream to downstream. An energy head reduction was observed under the investigated configurations. Most of the head variation occurs in the central part of the weir. Finally, the flow power decreases along the weir according to a non-linear function.A thorough knowledge of the flow field features should allow to improve side weir analysis and design, whatever approach is used for the study.     

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 (C_d). Different input combinations were predicted using the variables of H/P, P/L_e, and W/L_e 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/L_e, and W/L_e) 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 C_d by improving the prediction results of the implemented models.     

Discharge coefficient of rectangular sharp-crested side weirs,Part I: Traditional weir equation

A comprehensive study was performed to examine the flow characteristics over rectangular sharp-crested side weirs based on the traditional weir equation. To obtain a generally convenient discharge coefficient relationship, series of experiments were conducted according to manipulation of different prevailing parameters. The flow regime was consistently subcritical for upstream Froude numbers ranging from 0.08 to 0.91. Furthermore, experimental data sets of the former investigators were also applied. In order to identify the most important parameters affecting the discharge coefficient of rectangular sharp-crested side weirs, a sensitivity analysis was carried out based upon an artificial neural network modeling. Results of the sensitivity analysis indicated the Froude number to be the most influential parameter on discharge coefficient. Accordingly, a power equation is derived for estimating the discharge coefficient, which is applicable for both sub- and supercritical flow conditions simultaneously. Moreover, considering all the influential parameters, a nonlinear correlation was obtained with the highest precision to determine the discharge coefficient of sharp-crested rectangular side weirs.     

Experimental and numerical investigation of self-priming siphon side weir on a straight open channel

Siphons are basic and powerful hydraulic instruments which can be used as dam spillway or weir. In a siphon, atmospheric pressure pushes the water into the region of vacuum at the crest of the siphon, and then water falls towards the outlet of siphon. In this study, the siphon used as a side weir was investigated to determine hydrodynamic characteristics experimentally, theoretically and numerically. First, the flow properties of main channel were examined for subcritical flow condition. Then, the velocity and pressures distributions inside the siphon; finally the discharge performance of siphon side weir was determined comparatively, and the results were discussed.     

Support vector regression for modified oblique side weirs discharge coefficient prediction

Accurate determination of discharge coefficient is one of the major concerns in the process of the designing of side weirs. Relation between the modified side weirs discharge coefficient to various geometric and hydraulic situations leads to a high flow complexity around the weirs. In this study, two types of support vector regression (SVR) methods were employed to model the discharge coefficient of a modified triangular side weir. Two types of SVR are obtained by using the radial basis and polynomial as the kernel functions. Six different non-dimensional input combinations with different input variables were used to find the most appropriate one. The results show that both SVR-rbf and SVR-poly methods perform better when the number of input variables is higher, and there is no compaction in the non-dimensional input variables. Comparison between the investigated models shows that the SVR-rbf by RMSE of 0.063 performs much better that SVR-poly by RMSE of 0.084.     

Experimental investigation of discharge coefficient over novel kind of sharp-crested V-notch weir

Thin-plate weirs are the simplest and least expensive devices, which frequently have been employed in many water projects. In this research, a unique type of Sharp-Crested V-notch weir, entitled SCVW, has been introduced. The hydraulic characteristics of the present weir were investigated theoretically and experimentally under free aerated and non-aerated flow conditions in an open channel for large physical models. To investigate the variations of the discharge coefficient of SCVW versus weir height and vertex angle, a comprehensive laboratory experiments were conducted by measuring the discharge and the water head over the crest of weir. Possibility of different formulations for the head- discharge relationship of SCVW was examined and suitable analytical equation was proposed. The computed discharge using the suggested equation was within 0–10% of the observed ones. According to the experimental observations, the SCVW showed better performance in comparison with normal wire.     

Discharge equation of semi-circular side weirs: An experimental study

Side weirs are diverting structures and usually used for diverting and controlling the water flow into the side open channel. The present study deals with an experimental study regarding the hydraulic performance of side weirs with semi-circular vertical sections along the main channel. As flow depth of the main channel increases the top flow width of the semi-circular side weir (SCSW) increases which is an advantage when high discharge enters the main channel and should be immediately diverted for safety reasons. In this study, the flow discharge of semi-circular sharp-crested side weirs and their affecting parameters are investigated. To investigate the hydraulic behavior and geometric characteristics of the SCSWs, a comprehensive laboratory study including 155 tests (for three weir diameters 0.25, 0.30 and 0.40 m) was conducted in a physical model under subcritical flow conditions. Flow discharge of the SCSW was investigated in relation to height, diameter and flow head of side weir, also approach Froude number (Froude number at upstream end of the side weir) and main channel width. Three different discharge models were developed based on; purely dimensional analysis technique, classical weir equation with linear water surface and classical weir equation with horizontal water surface profile (conventional weir theory along with dimensional analysis technique). The presented mathematical discharge models enable estimation of discharge along the SCSW with acceptable accuracy (best model has an average error of 1.87% with a maximum error of 6.31%) compared with the measured data under subcritical flow conditions. Additionally, a relationship was proposed for computing the limiting flow depth at the downstream end of the SCSW. Experimental results confirm that the proposed relationship well explains the behavior of flow over the SCSW regarding the downstream flow conditions.     

Potential of particle swarm optimization based radial basis function network to predict the discharge coefficient of a modified triangular side weir

Estimating the discharge coefficient is one of the most important steps in the process of side weir design. In this paper, the particle swarm optimization algorithm and radial basis neural network are combined (RBFN-PSO) and employed to model the discharge coefficient of a modified triangular side weir. The developed RBF network has five neurons in the input layer and one neuron in the output layer. The inputs include a wide range of non-dimensional geometrical and hydraulic parameters of a modified triangular side weir, and the output is the discharge coefficient. The RBFN-PSO performance is evaluated using published experimental results and compared with the backpropagation radial basis function network (RBFN-BP) by using the statistical indexes Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and average absolute deviation (%δ). According to the results, the PSO algorithm successfully improved the RBFN while the RBFN-PSO model’s generalization capacity enhanced, with RMSE of 0.071 compared to the RBFN-BP model with RMSE of 0.114 in the testing dataset.     

Discharge characteristics and structure of flow in labyrinth weirs with a downstream pool

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

Prediction of the discharge of side weir in the converge channels using artificial neural networks

Considering the common use of side weirs in irrigation and drainage networks, estimation of the discharge of the side weirs has always given a consideration by water engineering researchers. Another issue about side weirs is the change in flow conditions in the weir and downstream channel. To optimize the flow conditions in the side weir, this structure is established in a converging channel to reduce the channel width and compensate the reduced discharge. The geometrical parameters assumed as variables in this study are: weir length, weir height, convergence angle and downstream channel width. About 248 experiments were performed. Three neural network models were used to estimate the discharge from the side weir. The model was constructed using MATLAB, and the dimensionless variables that were the geometrical and hydraulic ratios of the model were selected as input parameters. Four ratios were selected as inputs to the model to estimate the discharge coefficient and the discharge from the weir. Considering the outputs of the model, the neural-fuzzy networks have the least error compared to the other models, and this model estimates the discharge of side weir overflowing with 99.8% accuracy.     

Discharging capacity of rectangular side weirs in straight open channels

A side weir is a hydraulic control structure used in irrigation and drainage systems and combined sewer systems. A comprehensive laboratory study, including 843 tests for the discharge coefficient of a sharp-crested rectangular side weir in a straight channel, was conducted in a large physical model under subcritical flow conditions. The discharge coefficient is a function of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth. An equation was developed considering all dimensional parameters for discharge coefficient of the sharp-crested rectangular side weir. The average error of the proposed equation is 4.54%. The present study data were compared with ten different discharge coefficient equations developed by several researchers. The study also presents water surface profile and surface velocity streamlines.     

Flow measurement using a triangular broad crested weir theory and experimental validation

The self-cleaning and semi-modular triangular broad-crested weir without crest height was firstly subjected to a rigorous theory. The main objective was to establish the discharge relationship as well as that of the resulting discharge coefficient. For this, both energy equation and momentum equation applied between two judiciously chosen sections were necessary and proved to be essential. Contrary to previous studies related to flow metering, the relationship governing the flow rate was established by taking into account the approach flow velocity. Secondarily, the device was subjected to an intense experimental program to confirm the validity of the proposed theoretical relationships. It was observed an excellent agreement between the experimental and theoretical values of the flow rate. It has been found that the experimental and theoretical flow rates are related by a linear relationship such that $Q_{Exp}=1.0057Q_{Th}$. The constant clearly indicates that the flow rate theoretical formula only needs a slight correction. The theoretical stage-discharge formula was then very accurate even no calibration parameter was employed. The theoretical development has shown that the discharge coefficient C_d only depends on the dimensionless parameter M₁ that reflects the effect of the contraction of the cross-section of the approach channel. The variation curve of C_d(M₁) showed that C_d increases in the range [0.233; 0.277] with the increase in M₁.     

Performance evaluation of two different neural network and particle swarm optimization methods for prediction of discharge capacity of modified triangular side weirs

Technical design of side weirs needs high accuracy in predicting discharge coefficient. In this study, discharge coefficient prediction performance of multi-layer perceptron neural network (MLPNN) and radial basis neural network (RBNN) were compared with linear and nonlinear particle swarm optimization (PSO) based equations. Performance evaluation of the model was done by using root mean squared error (RMSE), coefficient of determination (R²), mean absolute error (MAE), average absolute deviation (δ) and mean absolute relative error (MARE). Comparison of the results showed that both neural networks and PSO based equations could determine discharge coefficient of modified triangular side weirs with high accuracy. The RBNN with RMSE of 0.037 in test data was found to be better than MLPNN with RMSE of 0.044 and multiple linear and nonlinear PSO based equations (ML-PSO and MNL-PSO) with RMSE of 0.043 and 0.041, respectively. However, due to their simplicity, PSO based equations can be sufficient for use in practical cases.