Experimental study for measuring discharge through compound broad crested weir

This paper deals with a new compound broad crested weir for measurement of discharge. Calibration of broad crested weir is mainly dependent upon the length of the weir crest (L), weir height and upstream water head over weir crest (h). Hence measurement of discharge varies as per change in the flow characteristics due to change in the geometry of weir for a given flume. Based on experimental analysis, past researchers have shown that discharge coefficient (C_d) changes proportionally with h/L ratio, maintaining an average range of C_d for various h/L values. In the present study a novel approach towards design of compound broad crested weir is proposed which can effectively measure wide range of discharges thereby maintaining a constant discharge coefficient irrespective of the head over weir. Experimentation has been carried out in a laboratory horizontal tilting flume 2.5 m long, 20 cm wide and 30 cm deep. The investigation is carried out for discharge ranging from 10 lps to 2 lps. In the earlier experimentation conducted C_d was varying in the range from 0.518 to 0.648, after which the broad crested weir model is modified for suiting best results thereby resulting in the reformed discharge coefficient values of 0.546–0.599 which is in close proximity to the design input value of 0.6.     

Sensitivity analysis of the factors affecting the discharge capacity of side weirs in trapezoidal channels using extreme learning machines

Side weirs are installed on the side walls of main channels to control and regulate flow. In this study, sensitivity analysis is planned using Extreme Learning Machines (ELM) to recognize the factors affecting the discharge coefficient in trapezoidal channels. A total of 31 models with 1 to 5 parameters are developed. The input parameters are ratio of side weir length to trapezoidal channel bottom width (L/b), Froude number (Fr), ratio of side weir length to flow depth upstream of the side weir (L/y₁), ratio of flow depth upstream of the side weir to the main channel bottom width (y₁/b) and trapezoid channel side wall slope (m). Among the models with one input parameter, the model including Froude number modeled the discharge coefficient more accurately (MAPE=4.118, R²=0.835). Between models with two input parameters, the model using Fr and L/b produced MAPE and R² values of 2.607 and 0.913 respectively. Moreover, among the models with four input parameters, the model containing Fr, L/b, L/y₁ and y₁/b was the most accurate (MAPE=2.916, R²=0.925).     

Experimental analysis of flow characteristics over hydrofoil weirs

The rounded crested weirs are commonly used for discharge measurements and this overflow structures have advantages such as stable overflow pattern and good accuracy. Hydrofoil weirs with streamlined properties are similar to the ogee weirs and can be used as a spillway profile. The hydraulic features of flow over hydrofoil weirs created by the NACA0018, NACA0021 and NACA0024 hydrofoil geometry placed in an open channel are investigated experimentally under free-flow conditions. The velocity field of hydrofoil weir flows are measured by one-dimensional Laser Doppler Anemometer. Experimental velocity profiles are measured along the middle section of the channel, especially around the weir structure, to determine the boundary layer separation. According to the determination of optimum weir structure the free surface profiles, pressure distributions on weir surfaces, experimental discharge coefficients and head losses over weir structures are determined for different structure and flow conditions. Pressure distributions over the hydrofoil weir are presented. In addition, the relationships between discharge coefficient (C_d) and flow rate (Q), specific total head (H/R), relative weir height (P/H), relative total head (H/P) and dimensionless total energy head upstream of the weir (H/L) are investigated.     

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.     

A hybrid ensemble machine learning model for discharge coefficient prediction of side orifices with different shapes

Side orifices are widely applied for flow control and regulation in channel systems. Accurate estimation of the discharge coefficient of the side orifice is significant for water management. The main objective of current research is to accurately predict the discharge coefficients of circular and rectangular side orifices. Considering that traditional empirical regressions are hard to estimate the discharge coefficient precisely due to the complex nonlinear relationship between the discharge coefficient and relevant parameters, a new hybrid boosting ensemble machine learning model, BO-XGBoost, is developed, which combines the advantages of the boosting ensemble model (XGBoost) and Bayesian Optimization. To further evaluate the proposed hybrid model, it is also compared with other tree-based machine learning models, including standalone XGBoost, Random Forest (RF) and Decision Tree (DT). Literature experimental data of the flow and geometric parameters relevant to the discharge coefficients of circular and rectangular side orifices are collected and applied to develop the models. Four dimensionless parameters of the relative channel width (B/L), the relative bottom height (W/L), the relative upstream depth (Y/L) and the upstream Froude number (Fr) are taken into consideration for the prediction of discharge coefficient (C_d). Furthermore, four different input combinations are designed and then compared to determine the best one on the basis of RMSE. By using the optimal input combination, our results demonstrate that BO-XGBoost provides the best comprehensive performance among all the involved machine learning models in the discharge coefficient prediction for both types of side orifices. Besides, the uncertainty analysis also reveals that BO-XGBoost shows the narrowest uncertainty bandwidth and gives the highest prediction reliability.     

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.     

Experimental study of discharge coefficient of trapezoidal arced labyrinth weirs of widened middle cycle

Arced labyrinth weir is a certain type of nonlinear weirs with a very high discharge capacity. Thanks to the increased effective length and the ensuing increased discharge capacity of these weirs, they can be used in dam spillways and water regulating structures. This study focused on trapezoidal Arced labyrinth weirs (TALW) of widened middle cycle. Various experiments were performed to evaluate the effect on discharge coefficient of various geometric parameters, including the ratio of inside apex width of the end cycles to that of the middle cycle (w₂/w₁) and the ratio of the length of labyrinth weir (Apron) in flow direction to the width of the middle cycle (B/w₁). Results of this study showed that with a decrease in w₂/w₁ from 0.42 to 0.30, discharge coefficient (C_d) would increase by 13–33%.     

Flow velocity pattern around trapezoidal piano key side weirs

In general, the side weirs are the structures installed along a channel or river. When the flow depth rises above the weir crest, the overflow passes through these weirs and enters the lateral canal. Nowadays, piano key weirs are considered as an important alternative to labyrinth weirs to modify the weirs encountering with difficulty to pass the maximum flow discharges. The present study investigates the hydrodynamic performance and the effect of the uniformity of velocity field on the resultant kinetic energy in the trapezoidal piano key side weirs with 90° installed laterally in the main channel wall. These weirs are classified as A-Type piano key weirs and two approaches (main: Mode 1 and adverse: Mode 2) were used to investigate the effect of the weirs' placement on their performance. The results showed that for velocity vectors in both modes, on average, the maximum flow discharge through the side weir occurred in the x and y directions (V_x and V_y) at Z*<0.2 and 0.2<Y*<0.7. The results also showed that at the control surface of X* = 1, the maximum values of α occur due to existing the inverse flow and increasing the deflection angle of the velocity vectors. The performance of the weir in Mode 2 was more appropriate Mode 1 due to the lack of weir base at the flow inlet, which is an obstacle for the deflection angle of the velocity vectors.     

Experimental study of discharge coefficient for trapezoidal piano key weirs

Piano Key Weirs (PKW) have been invented in the last decade to increase discharge capacity of hydraulic structures. Despite extensive studies on this type of weir with a rectangular plan form (RPKW), there are only a few pieces of research addressing trapezoidal piano key weirs (TPKW). In this experimental study, geometrical parameters of TPKW models were varied under different flow conditions and effects on discharge coefficient (C_d) were investigated. The C_d values were found to be mostly influenced by L/W whereas W_i/W_o had the least effect. Results also showed that TPKW has higher discharge efficiency in comparison with RPKW. This was believed to be related to formation of an “interference wedge” over the TPKW. Finally, quantitative values for distinguishing three flow regimes (i.e. nappe, transition and submergence) as well as criteria for design of TPKW are proposed.     

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.     

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.     

Radial Basis Neural Network and Particle Swarm Optimization-based equations for predicting the discharge capacity of triangular labyrinth weirs

Conventional weirs are utilized for controlling, measuring and adjusting the flow depth in hydraulic structures, such as those found in irrigation and drainage networks. Various weirs with modified shapes are utilized to increase the discharge capacity. The main goal of this study is to investigate the discharge coefficient (C_d) of triangular labyrinth weirs using soft computing methods. The performance of the Radial Basis Neural Network (RBNN) is compared with that of Multiple Nonlinear and Multiple Linear Particle Swarm Optimization (MNLPSO and MLPSO). Models developments are conducted using published experimental data from the literature. Comparing the RBNN, MLPSO and MNLPSO results obtained through these soft computing techniques with experimental data shows that all models perform well in predicting the discharge coefficient of a triangular labyrinth weir. Performance of the proposed approaches which demonstrated explicit equation given by MNLPSO model provided the discharge capacity with lower error (RMSE=0.0223) is compared with the MLPSO (RMSE=0.0346) and RBNN (RMSE=0.045) approaches.     

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.     

Studying the relationship between the hydraulic and geometry characteristics of labyrinth weirs based on the historical memory of reported data

One of the effective ways to increase the efficiency of weirs is to use nonlinear weirs, such as labyrinth weir, which increases the flow capacity by increasing the length of the weir at a fixed width. Given the importance of precisely estimating the flow discharge coefficient of this type of weir and its impact on supplying the safety of water structures, in the present study, the flow coefficient of labyrinth weirs was estimated using data-driven models of Extreme Learning Machine (ELM), Classification And Regression Tree (CART), Chi-square Automatic Interaction Detector (CHAID), and Multiple Linear Regression (MLR). After the modeling process, the predicted results were compared with the observed values using statistical measures and diagnostic analysis. In this study, three input combinations of hydraulic parameters, including the total upstream hydraulic head of weir (H_T), weir discharge (Q), and head to weir height (H_T/P) were used as input vectors. In order to evaluate the accuracy of the models, the statistical indicators of Coefficient of Efficiency (CE), RMSE, MDE, and RSD were employed. The final results showed that the ELM method created with all potential input parameters (H_T, Q, and H_T/P) was highly accurate in determining flow discharge coefficient. Due to having the lowest error (CE = 0.8815, RMSE = 0.0370), it was selected as the superior model.     

Effect of anti-vortex structures installed on stepped labyrinth side weirs on discharge capacity

Side weirs are essential structural elements commonly used to control water levels in rivers and canals. If the length of the opening is limited, a labyrinth side weir can be used to increase the amount of water diverted out of the channel and the effective length. This research studied the influence of installing an antivortex structure in stepped labyrinth side weirs on discharge capacity. It has four types of antivortex installed in different hydraulic conditions at different Froude numbers, dimensionless crest height, dimensionless weir opening length, step number, and head angle. Using data from 168 experimental runs without antivortex to allow comparison and 672 experimental runs to determine the best performance of antivortex structures that improved discharge capacity, and 528 runs measured velocity to investigate the intensity of secondary currents generated by lateral flow and other hydraulic conditions, including water surface profiles. According to the research results, installing antivortices regulated the flow, significantly improved the efficiency of the single-cycle stepped labyrinth side weir, and lowered secondary flows caused by interaction with the vertical axis. Finally, the discharge coefficient improves to 18% after analyzing the best type of antivortex, considering shape and height.     

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.     

Experimental study of effect of creating an additional cycle along the lateral crest of the labyrinth weirs

One of the practical and economical ways to enhance the discharge capacity is to use labyrinth weirs. The longer crest length in labyrinth weirs than in linear weirs has caused these weirs to have both a higher discharge coefficient and water discharge capacity than a linear weir. In the present study, the discharge coefficient of trapezoidal and triangular labyrinth weirs was investigated by creating an additional cycle along the lateral crest of the weir. By constructing 10 physical models of labyrinth weirs, tests were performed in the hydraulic and sediment laboratory of the Khuzestan Water and Power Authority (KWPA). Dimensional analysis by the Buckingham method revealed the discharge coefficient (Cd) as a function of variable parameters such as the total hydraulic head to weir height ratio (Ht/P) and weir shape factor (Sf). The results of experimental tests showed that at the hydraulic head ratio (Ht/P) of 0.1, the TP weir had a higher discharge coefficient of 3.5% than the TPTPO weir and 2.5% than the TPTRO weir. However, at a hydraulic head ratio of 0.12, the TR weir had a lower discharge coefficient of 4.6% than the TRTPO weir and 6.9% compared to the TRTRO weir. For the hydraulic head ratio of 0.14, the TRTPI weir was 5.8% and the TRTRI weir was 9.4% higher than the TR weir. Statistical analysis using SPSS indicated that TRTPO and TPTRO weirs had the highest correlation with the cubic model.     

Study of flow at side weir in narrow flume using visualization techniques

The purpose of the research was to quantify characteristics of a subcritical flow at a rectangular sharp-crested side weir in a rectangular main channel using non-invasive measuring techniques based on the visualization of the flow. Experiments were carried out in physical models, including nine different dimensions of the side weir and nine combinations of the inflow and tailwater level for each weir, amounting to 81 test runs. Velocity vector fields were measured in various horizontal planes along the side weir using a high speed digital camera and electrolysis-induced hydrogen bubbles as flow tracers. Recorded films were converted into sequences of images which were used for numerical calculation of local velocities. Components of velocity vectors were determined with great spatial and time resolution. Longitudinal profiles of water surface elevation at each side weir were determined using photos of laser-induced vertical section planes. Measured discharges and flow depths were used to formulate new equation for the side weir discharge coefficient using dimensional analysis. The principal results indicated that velocity distribution along the side weir was distinctly non-uniform, with various velocity ratios increasing along the crest. However, the calculated energy grade line was parallel to the main channel bed, indicating that only friction losses were present. The proposed equations for the side weir discharge coefficient gave results that were in good accordance with two other studies.     

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.