Weir Discharge Research Articles

Experimental investigation of slit weir discharge

ABSTRACT A rectangular slit weir is used to measure small flows, namely, those flows less than 5 L/s and contraction ratios (b/B) less than 0.25. In the present study, flow tests were conducted in a laboratory setup with various contraction ratios (b/B) under models A (b/B = 1/12), B (b/B = 1/8), C (b/B = 1/6), D (b/B = 5/24), and E (b/B = 1/4). The dimensional analysis revealed that b/B, the height of the flow on the crest of the weir to the height of the weir crest (h/P), the Reynolds number (Re), and the Weber number (We) are effective parameters for predicting the discharge coefficient of the slit weir. The experimental results indicated that the discharge coefficient is variable for different contraction ratios; the maximum average discharge coefficient was achieved at the lowest b/B (Model A), with a value of 0.72. The minimum average discharge coefficient obtained in Model B equals 0.639. In addition, former prediction equations were compared with the obtained experimental data, and the minimum, average, and maximum errors were calculated. Furthermore, a relationship was established for deriving the discharge coefficient in slit weirs with R2 = 0.9212, RMSE = 0.02244, and MAE = 0.0134 based on the obtained experimental data with four effective parameters, b/B, h/P, Re, and We.

Numerical and sensitivity analysis of hydraulic characteristics of triangular labyrinth side weir

Triangular labyrinth side weirs have significantly more discharge capacity than traditional nonlinear weirs, and the complex hydraulic parameter interaction mechanism has been the research focus. This study used Computational Fluid Dynamics (CFD) to analyze the side weir's flow characteristics. Then, the Bayesian optimization algorithm and Extreme Learning Machine (BELM) developed a prediction model for the side weir's discharge coefficient. Finally, Sobol's method performed a sensitivity analysis for hydraulic parameters. The results show that the main channel's streamline is evenly distributed and begins to shift when it is close to the side weir. The overflow front is increasing and secondary flow also increases. BELM's Mean Absolute Percentage Error and Root Mean Square Error are 8.793 % and 0.455 in the testing stage, respectively, declined by about 56.24 % and 32.29 % compared with ELM; Froude number Fr, weir crest angle θ and the ratio of overflow front length to weir head l/h1 are the most critical hydraulic parameters affecting the discharge coefficient, the global sensitivity coefficients are 0.4393, 0.4218 and 0.4152, respectively.

Application of machine learning models in predicting discharge coefficient of side B-type piano key weir

Side weir is a hydraulic structure within a channel which is usually used to discharge excess water, to divert the flow, and to regulate water surface levels in rivers and irrigation and drainage networks. In general, piano key weirs (PKW) have been used as weirs perpendicular to the flow direction in straight channels. However, the use of the PKW as a side weir in the outer arch of the channels is a new approach to enhance the weir's performance. In this study, 289 tests were first performed on the B-type rectangular side piano key weir (RSPKW) at two arc angles of 30 and 120°. Then, Fuzzy Inference System (FIS), Adaptive Neuro-Fuzzy Inference System (ANFIS), ANFIS and Teaching Learning Based Optimization (TLBO), ANFIS and Grasshopper Optimization Algorithm (GOA), Extreme Learning Machine (ELM) and Outlier Robust ELM (ORELM) models were used to predict the weir discharge coefficient. The results showed that two optimization models of TLBO and GOA increased the accuracy of the ANFIS model. The results showed that the ANFIS-GOA model has accuracy of Root Mean Squared Error (RMSE) = 0.0361, Coefficient of determination (R2) = 0.9772, and Kling Gupta coefficient (KGE) = 0.9858. The ANFIS-TLBO, ANFIS, and FIS models were ranked, respectively. Also, the results showed that ELM and ORELM models have accuracy close to ANFIS-GOA and can be a suitable alternative for complex fuzzy models. According to the statistical analysis, it was found that the parameters of the ratio of weir height to flow depth at the upstream edge of weir (P/h1), arc angle (α), and the ratio of height of the foundation to the main channel width (pd/B) had the greatest role in the development of the models, respectively.

Integrated learning model for water intake capacity of Tyrolean weirs under supercritical flow

ABSTRACT Tyrolean weir can be used as an effective solution to address floatation and sediment deposition in runoff hydropower stations. To improve the efficiency and accuracy of calculating this structure's water intake capacity. The integrated learning algorithm random forest (RF), the firefly algorithm (FA), and the exponential distribution algorithm (EDO) are utilized to develop the algorithm that can be used for the Tyrolean weir Cd and (qw)i/(qw)T prediction models. Sobol's method and SHAP theory are introduced to analyze the above parameters quantitatively and qualitatively. It is shown that EDO-RF is the optimal prediction model for the Tyrolean weir's discharge coefficient and the Froude number Fr has the greatest influence on the Cd prediction results; when Fr < 30, the greater the negative influence of Fr on the model prediction results. When Fr > 30, the greater the positive influence of Fr on the model prediction results. FA-RF is the optimal prediction model for the Tyrolean weir water capture capacity (qw)i/(qw)T, with the ratio of bar length to bar spacing L/e being the largest; When L/e < 20, the greater the negative influence of L/e on the model prediction results. When L/e > 20, the more significant the positive impact of L/e on the model prediction results.

Equations and methodologies of inlet drainage system discharge coefficients: A review

Abstract Accurate determination of grate inlet discharge coefficients is crucial in reducing modeling uncertainties and mitigating urban flooding hazards. This review critically examines the methods, equations, and recommendations for determining the weir/orifice discharge coefficients, based on the inlet parameters and flow conditions. Reviewing previous studies for inlets showed that the discharge coefficient of rectangular inlets under subcritical flow ranges from 0.53 to 0.6 for weirs and from 0.4 to 0.46 for orifices, while in grated circular inlets, it falls between 0.115 and 0.372 for weirs and between 0.349 and 2.038 for orifices. For circular non-grated inlets under subcritical flow, the weir and orifice coefficients are in the range of 0.493–0.587 and 0.159–0.174, respectively. However, the orifice discharge coefficients of grated and non-grated inlets with unknown Froude number range between 0.14–0.39 and 0.677–0.82, respectively. For supercritical flow, the weir and orifice discharge coefficients of grated and non-grated rectangular inlets are 0.03–0.47 and 1.67–2.68, respectively. Previous studies showed that it is recommended to correlate the discharge coefficients with the approaching flow and Froude number under subcritical and supercritical flows, respectively. Yet, additional studies are recommended for a better understanding of the limits and parameters governing the flow transitional stage between weir and orifice and between subcritical and supercritical conditions. Moreover, further research is required to determine the weir and orifice discharge coefficients of circular inlets under supercritical flow as well as the orifice discharge coefficient range of rectangular non-grated inlets under subcritical flow. Finally, it is recommended to increase the road surface roughness to reduce Froude number, and thereby, increase discharge coefficients of street inlets. The aim of this review is to help inlet designers and authorities promote sustainable cities with resilient urban drainage systems and reduce the environmental, economic, health, and social impacts of urban drainage failure.

The calibration of sharp-crested weirs with a horizontal edge used for measuring flows in partially full pipes

This paper presents the results of a laboratory study on the discharge capacity of sharp-crested weirs fitted with a horizontal edge in pipes during open-channel flow conditions and clean water used to measure the outflow. Such sharp-crested weirs are mounted in pipes and are used to control the inflow to separators. The stream profile does not correspond to the profile given by Bazin for sharp crested weirs in channels. A desired location of the water level measurement point for flow rate calculations was provided. Discharge curves were identified for three sharp-crested weirs of 0.0465, 0.0634 and 0.0771 m in height, installed in the pipe of 0.1534 m in diameter and inclinations of 0.5 and 1.0%. The discharge curves for weir flow with free nappe does not show a significant effect of the pipe slope on the weir discharge capacity. The non-dimensional formulas for the discharge capacity of the sharp-crested weir were found as general polynomial regressions. The results indicate that the calibrated sharp-crested weir with a horizontal edge placed in a pipe can be used to control the flow. Due to the scale effect, relationships obtained from the calibration cannot be generalised to other pipe diameters and weirs heights than those analysed.

A performance comparison of the meta model methods for discharge coefficient prediction of labyrinth weirs

Weirs are hydraulic structures with various applications, such as flow measurement, flow diverting, and/or flow control. Labyrinth weir as a nonlinear weir with a folded crest enhances the spillway system discharge capacity by increasing the crest length for a given channel width. As a remarkable parameter, the discharge coefficient plays an important role in determining weirs' passing capacity. So, it is important that the discharge coefficient be accurately represented to ensure an appropriate and economical design. This research evaluates the prediction accuracy of four soft computing techniques, such as support vector machines (SVM), gene expression programming (GEP), software (QNET), and artificial intelligence networks (ANN), to predict the discharge coefficient of labyrinth weirs using three different scenarios. The model's input parameters included the total water head ratio (HT/P), magnification (Lc/W), and cycle wall angle (α). On reviewing the outcomes of the developed models, it appeared that each of them demonstrated satisfactory performance in predicting the discharge coefficient. However, ANN and SVM reveal more accuracy compared to other techniques. The prediction results reveal that the ANN as a superior model has the following performance metrics: R2 = 0.998, DC coefficient = 0.996, and RMSE = 0.006. The sensitivity analysis results indicate that HT/P is the most effective factor in determining the labyrinth weir discharge coefficient in all methods. This suggests that the ratio of HT (total water head) to P (weir height) has a significant impact on the overall model performance. Upon comparing the results of this research with those of other researchers, it is evident that the evaluation indicators for all methods employed in this study are relatively superior.

Predicting discharge coefficient of weir–orifice in closed conduit using a neuro-fuzzy model improved by multi-phase PSOGSA

This study investigates the viability of a strong algorithm (PSOGSA) merging particle swarm optimization (PSO) and gravity search algorithm (GSA) in tuning adaptive neuro-fuzzy system (ANFIS) parameters for modeling dimensionless experimental discharge of combined weir–orifices. The results are compared with the standard ANFIS and two hybrid models ANFIS tuned with PSO and GSA. The models are assessed by applying several dimensionless input parameters, consisting h/D (the ratio of upstream water depth to channel diameter), W/D (the ratio of orifice opening height to channel diameter), H/D (the ratio of plate height to channel diameter) and using comparison indices such as root-mean-square error and mean absolute error. The outcomes reveal that the new ANFIS-PSOGSA method provides superior accuracy in modeling dimensionless experimental discharge over the ANFIS-PSO, ANFIS-GSA and standard ANFIS method. Among the input parameters, the h/D was found to be the most effective input on modeling dimensionless experimental discharge while involving the H/D parameter deteriorated the models’ performances. The relative root-mean-square error differences between ANFIS-PSOGSA and ANFIS are found as 50% and 68.29% for pipe A and B, respectively. By implementing the ANFIS-PSOGSA, the accuracy of ANFIS-PSO and ANFIS-GSA is also improved in modeling dimensionless experimental discharge by 45.71% and 29.63% in pipe A and by 63.89% and 45.83% in pipe B with respect to root-mean-square error.

Uncertainty analysis of discharge coefficient predicted for rectangular side weir using machine learning methods

Abstract The present study used three machine learning models, including Least Square Support Vector Regression (LSSVR) and two non-parametric models, namely, Quantile Regression Forest (QRF) and Gaussian Process Regression (GPR), to quantify uncertainty and precisely predict the side weir discharge coefficient (Cd) in rectangular channels. So, 15 input structures were examined to develop the models. The results revealed that the machine learning models used in the study offered better accuracy compared to the classical equations. While the LSSVR and QRF models provided a good prediction performance, the GPR slightly outperformed them. The best input structure that was developed included all four dimensionless parameters. Sensitivity analysis was conducted to identify the effective parameters. To evaluate the uncertainty in the predictions, the LSSVR, QRF, and GPR were used to generate prediction intervals (PI), which quantify the uncertainty coupled with point prediction. Among the implemented models, the GPR and LSSVR models provided more reliable results based on PI width and the percentage of observed data covered by PI. According to point prediction and uncertainty analysis, it was concluded that the GPR model had a lower uncertainty and could be successfully used to predict Cd.

On the effect of flow regime and slope of the channel bed on the hydraulic performance of the sharp-crested rectangular side weir: a numerical simulation

The aim of this study is to numerically investigate the effect of bed slope on the hydraulic performance of side weirs in supercritical and subcritical flow regimes. Increasing the bed slope decreases the weir efficiency and discharge coefficient in the subcritical flow regime up to 14.54% and in the supercritical flow regime up to 9.26%. By examining the longitudinal velocity distribution, it was observed that in the subcritical flow regime, the maximum longitudinal velocity occurs at the beginning of the upstream of the side weir, and by moving towards the downstream of the weir, the flow velocity decreases and increases again after leaving the length of the weir. In the supercritical flow regime, it has an increasing trend when the flow enters from the upstream of the side weir. The increase in discharge coefficient with the increase of the weir height varied between 4.6% and 7.8%. With increase of the slope of the channel bed, the velocity along the length of the weir increases by 10.88% and 6.17%, respectively, in the subcritical and supercritical regimes, and the transverse velocity along the transverse direction for the subcritical and supercritical flow regimes decreased by 22.23% and 4.80%, respectively.

Evaluating performance of various methods in predicting triangular sharp-crested side weir discharge

This paper investigated the efficiency of the traditional weir equation (TWE), Domínguez, adjusted Domínguez, and Schmidt approaches, as an alternative to the De Marchi procedure, for computing discharge of a sharp-crested triangular side weir. Comprehensive experimental data were used for the analysis, including 342 data from the present study and 140 data from other sources. The effects of approach Froude number Fr1, the ratio of weir height to upstream flow depth p/y1, and weir apex angle θ on the discharge coefficients obtained from different methods were studied. Sensitivity analysis using the partial swarm optimization-support vector regression method indicated that Fr1, p/y1, and θ affect the discharge coefficients. It was found that Fr1 with sensitivity indices equal to 1.89, 3.74, and 4.04 has the most substantial effect on the De Marchi coefficient, TWE coefficient, and adjusted Domínguez coefficient; meanwhile, p/y1 has the most significant impact on Domínguez coefficient and Schmidt coefficient with sensitivity index equal to 1.57. In addition, it was found that θ had the lowest sensitivity indices in estimating discharge coefficients. New equations for forecasting sharp-crested triangular side weir discharge coefficient were presented based on dimensional analysis. The new De Marchi coefficient executed better for calculating triangular side weir discharge than earlier De Marchi coefficients. Moreover, TWE, Domínguez, adjusted Domínguez, and Schmidt methods performed better than the De Marchi procedure (with MSE = 4.581) in calculating sharp-crested triangular side weir discharge. However, considering the simplicity of the TWE approach compared to other methods, this approach with R2 = 0.975, NSE = 0.975, MSE = 3.610, MRE = 0.097, and CP10% = 71.36 was introduced as the superior procedure.

Experimental hydraulic parameters of drainage grate inlets with a horizontal outflow in the broad-crested weir mode.

The accurate assessment of discharge coefficients for different types of water inlets is crucial for minimizing modelling errors in drainage systems thus reducing the risk of flooding in adjacent areas. This study experimentally investigated the hydraulic characteristics of gully grate inlets with water seal and horizontal outflow, with nominal outlet pipe diameters of 100 and 150 mm, using a laboratory setup that meets the requirements of a special European regulation. Transition depths from the weir to the orifice mode were determined, and it was found that the perforated grates significantly increased the hydraulic resistance compared to the bar grates, resulting in a corresponding decrease in the discharge capacity of gully inlets. Power-law relationships between the weir discharge coefficient and gauge head were obtained for both bar and perforated grate inlets, as well as between the discharge coefficient and Froude number at the perimeter of grate inlets. These findings provide important insights for optimizing the design and performance of water inlets, particularly in the weir mode, which is critical for the proper functioning of drainage systems.

Experimental and numerical investigation on the hydraulic design criteria for a step-pool nature-like fishway

Hydraulic considerations specific for the design of step-pool nature-like fishways (NLFs) are limited to the body dimensions of the target species. Additional hydraulic criteria for flow depth, maximum values for each of pool depth, velocity, and turbulent kinetic energy in terms of the weir opening width and discharge can help design an optimum step-pool NLF. The present study developed design charts and rating curves based on numerical modeling using the computational fluid dynamics software FLOW-3D® HYDRO. Instantaneous velocity measurements on a 1:4 scaled physical model of a step-pool nature-like fishway designed as per the available design guidelines have been used to validate the numerical model. The hydrodynamics of the fishway with respect to the weir opening ratio b r (0.10, 0.25, 0.45, 0.65, and 1.00) and discharge Q (0.1–1.5 m3/s) was analyzed through numerical simulations on a prototype scale. The simulation results showed that the maximum flow velocity and the averaged velocity over the crest at b r = 0.10 and 0.25 are considerably lower than at b r > 0.25. The maximum turbulent kinetic energy and energy dissipation factors for the tested range of discharges were within recommended limits for b r = 0.10 and 0.25. The present study outcome in terms of the design charts and rating curves that illustrate the relationship between different variables can be used for an optimum design and ease in field implementation. In addition, the bed structure of the step-pool NLF presented in this study can be used to recreate full-scale or pilot models.

Prediction of Coefficient of Discharge for Oblique Sharp Crested Weir using ANN Model

Abstract: The application of artificial neural networks for solving complex civil engineering problems is of huge importance. This paper presents some of the positive aspects of the neural network’s model that are used for the determination of the coefficient of discharge of oblique sharp crested weir. Sharp crested weirs are used to measure flow rate and control upstream water surface in irrigation canals and laboratory flumes. The main advantages of such weirs are ease of construction and capability of measuring a wide range of flows with sufficient accuracy. ANN models have been developed to predict the discharge coefficients of oblique sharp-crested weirs for free flow cases using Borgheiet al.’s experimental data.

Flow measurement by vegetated weirs: An investigation on discharge coefficient reduction by crest vegetation

Flow measurement using weirs as an engineered hydraulic control has been well studied and understood, but the presence of vegetation on the weir crest or top of weir-like structures in natural waterway has rarely been considered. This technical note presents a quantitative assessment of the effects of crest vegetation roughness on flow estimation. Experiments are carried out to record the discharge coefficient reduction of finite-crest-length weirs when the weir crests are covered by flexible artificial vegetation. The effects of equivalent roughness height of the vegetation canopy on the weir discharge capacity are evaluated, in addition to the variation of flow rate and weir crest length. According to the ratio of upstream head to vegetated crest length, the tested flows are classified as broad-crested and narrow-crested weir flows, and some change in discharge coefficient deterioration rate is observed for the two types of weir flows. Empirical equations are proposed for prediction of discharge coefficient thus flow estimate correction by taking into account the vegetation resistance effects. The results may contribute to improve the accuracy of hydrological modeling and flood forecasting, although vegetation degradation during floods is not considered.

Research into the pressureless flow in hydrotechnical systems at mining enterprises

Purpose. The research purpose is to develop a mathematical model of a pressureless flow in a channel with the occurrence in some areas of overflow layer through the wall. Using this model, it is possible to calculate the overflow layer height and length, as well as the change in flow rate in the channel due to the withdrawal of part of the fluid as a result of the overflow. Methods. The research uses a comprehensive multi-stage analytical approach. Firstly, in order to develop a mathematical model for a pressureless flow in the channel with the occurrence in some areas of overflow layer through the wall, this research analytically determines the dependence of the flow rate through the channel wall based on formulas for calculating the weir discharge coefficient. At the second stage, a mathematical model of a hydraulic mixture pressureless flow in a rectangular channel with an overflow through the wall is developed to determine the parameters and flow regimes of the stream. Findings. The dependences of the dimensionless height of the overflow through the channel wall and the effective critical flow depth on the dimensionless current channel length have been obtained for various values of the acting force parameters and the process parameter of the fluid overflow through the channel wall. This made it possible to study the dynamics of changes in these values along the channel for various values of the specified parameters, and to assess the degree of influence of the relevant factors on the characteristics of the pressureless flow along the channel and the process of fluid overflow through wall. Originality. For the first time, the model of the pressureless flow in the channel is generalized for the case of occurrence in some areas of overflow layer through the wall, when the length and height of the overflow layer are not determined by a hole in the side surface, but are controlled by a decrease in the corresponding flow rate. For the first time, this model makes it possible to calculate the height and length of the overflow layer and the change in the flow rate in the channel due to the withdrawal of part of the fluid as a result of the overflow in cases of overflowing condition of the channel with the stream under unstable and non-calculated flow regimes. Practical implications. The mathematical model and the calculation results can be used to ensure the environmental safety of the logistics systems of mining enterprises, as well as to assess the volume of the environmental pollution in case of overflowing through the wall of the channels of pressureless hydraulic transportation of waste from mineral processing and metallurgical plants.

On the Hydraulic Characteristics of Submerged Flow over Trapezoidal-Shaped Weirs

Abstract Subcritical flows over highway and railway embankments, commonly encountered during flood events, can be treated like submerged flows over trapezoidal-shaped weirs. In earlier studies, the equation of the submerged-flow discharge for such types of weirs was developed as a function of the degree of submergence and free-flow discharge. However, the application of this equation in practice requires a pre-determined discharge from experiments performed under free-flowconditions. In this study, a discharge equation was deduced from the streamwise momentum balance equation, which overcomes the drawback of the previous approaches. The results of the validation demonstrated that the proposed equation is capable of predicting the submerged-flow discharge of a trapezoidal-shaped weir within ±6.0% of the measured value. Furthermore, the most prominent features of the submerged overflows were examined by systematically analyzing the experimental data. For such flows, the free-surface and bed-pressure profiles are self-similar only over the upstream face of the weir. Results of this investigation confirmed that the degree of submergence and the slope of the downstream weir face significantly affect the characteristics of the submerged flow, but the effect of the latter on the non-modular discharge is marginal.

Assessment of coefficient of discharge of gabion weir using soft computing techniques

Assessment of coefficient of discharge of gabion weir using soft computing techniques

Evaluation of the hydraulic behavior of the composite hydraulic structure considering a bed flume with special obstacle

The experimental simulation between the composite hydraulic structure and the found obstacles in the downstream region is a challenging process due to the energy losses and kinematic dissipation. The current work focuses on a comparative analysis of free flow conditions that exist without obstacles and submerged flow conditions that occur due to obstacles. It indicates the evaluation of hydraulic variables and geometrical variables of composite hydraulic structure for both flow conditions. In addition, it includes an investigation of the interaction among these variables. The hydraulic variables include actual discharge, flow velocity, flow cross-sectional area that crosses the gate, downstream water depth, discharge coefficient, Reynolds number and, Froude number, while the vertical distance between the weir and gate represents the geometry variable. The interference between the weir discharge and gate discharge plays a significant role in the result fluctuation and variation for both flow conditions, while the form and size of the obstacles only have a major effect on the submerged flow. For both flow conditions, the water depth is investigated; there would be a drastic increase in water depth by using obstacles in the downstream area as compared with not using the obstacles. This study adopts different obstacles in shape and size, therefore, the variation of maximum and minimum water levels related to the location will occur.

The influence of projection angle on nappe stability at low energy heads over the weir crest

Abstract Under certain low head hydraulic conditions, weir discharge under gravity flow can produce an oscillating nappe characterized by horizontal waves and audible low-frequency acoustic energy, which in some cases can have a significant impact on the local environment. In an effort to better understand the mechanism behind nappe oscillation, an experimental investigation was conducted using a linear weir (1.83 m wide, 1.10 m in height, and 0.076 m in thickness) with four different crest shapes (rectangular, quarter-round upstream, half-round, and quarter-round downstream) at a wide range of unit discharge ranging from 8×10−3 m2/s to 36×10−3 m2/s. Using Particle Image Velocimetry (PIV) techniques, differential pressure measurements, and water surface profiles, the influence of Weber number, angle at which the nappe hits the downstream pool (angle of impact), and nappe projection angle on the nappe oscillation are reported. No significant relationship was found between the Weber number and nappe instability. The results suggest that the nappe is stable for unit discharge between 20×10−3 and 24×10−3m2/s regardless the shape of the weir crest. Also, the stable projection angle is −17° for rectangular and quarter-round upstream weirs and −35° for half-round and quarter-round downstream weirs for the specific tested weir.