Discharge characteristics of sharp-crested circular side orifices in open channels

A side orifice is a flow diversion structure provided in one or both side walls of a channel to spill/divert water from the main channel. It is widely used in irrigation and environmental engineering. Analytical and experimental studies related to the discharge characteristics of sharp-crested circular side orifices in open channels under free flow conditions have been presented in this paper. Considering the side orifice as large, the discharge equation for the side orifice is derived analytically. Experiments were performed to estimate the coefficient of discharge which depends on the approach flow Froude number and ratio of the diameter of the orifice and bed width of the channel. Relationships for the coefficient of discharge, considering the orifice as large and small were developed. Such relationships were used to compute the discharge through the orifice for data not used for proposing such relationships for the coefficient of discharge. The computed discharges were within ±5% of the observed ones. The average percentage error in computation of discharge through the orifice considering it as large and small are, respectively, 1.59% and 1.66% which are practically the same. Therefore, it is recommended that the discharge through the side orifice can be computed considering it as a small orifice within the range of data used in the present study.     

A review of studies on estimating the discharge coefficient of flow control structures based on the soft computing models

The discharge coefficient (Cd) plays a vital role in the accurate design and safety of weirs, spillways, and dams. In the last decade, Soft Computing(SC) models, which showed excellent capabilities for non-linear mapping between parameters, were widely used to estimate the discharge coefficient of flow control structures. This study provides a comprehensive review of the application of SC models for estimating Cd of different flow control structures such as ogee spillways, orifices, side weirs, etc. In addition, the most common empirical relations which are obtained from laboratory experiments are discussed briefly. The findings revealed that weir length/flow depth ratio, weir length/channel width ratio, weir height/flow depth, and Froude number are widely used to estimate Cd in the side weirs. Besides, the ratio of orifice crest height to height of side orifice, the ratio of main channel width to length of side orifice, ratio of main channel width to height of side orifice, and ratio of the height of side orifice to upstream flow depth were extensively employed to calculate Cd of orifice structures. The common parameters for measuring Cd of labyrinth weirs are, discharge over a labyrinth cycle, weir height, channel width, apex constant, upstream head, discharge over the weir, effective length, convergence constant, sidewall angle, and Froude number. In the weir-gate structure, some factors such as contraction coefficient of the gate, head loss, and weir height are key parameters for the accurate evaluation of Cd. The trends of SC models, features of popular models, and the background of models are discussed briefly in this paper. Also, research gaps and possible directions for new studies are suggested.     

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.     

Analytical and experimental study of flow through elliptical side orifices

Discharge estimation is important for water management. Side orifices are commonly used in irrigation and drainage networks for distributing the water. Despite the vast amount of theoretical and experimental studies published, no generally applicable discharge equations are available for elliptical sharp-crested side orifices. When the length (diameter) of the circular side orifice is not sufficient to divert the water, an elliptical side orifice is a good alternative. In this paper, the elliptical sharp-crested side orifices were studied theoretically and experimentally. Several models were developed to predict the discharge coefficient of elliptical side orifices based on the Buckingham's theorem of dimensional analysis. A series of laboratory runs (588 runs) were conducted for different values of orifice geometry. The main channel discharge used in the tests ranged from 13.8 to 39.6 l/s and the side orifice discharge ranged from 3.66 to 21.4 l/s and upstream Froude number ranged from 0.22 to 0.77. Using measurements obtained by laboratory runs carried out in this investigation the proposed models of elliptical side orifices were calibrated under free outflow conditions. The model that includes the approach Froude number had an average error of 1.74%, while other model that does not include the approach Froude number had an average error about 2.43%. Moreover, suitable models were proposed for design procedure when measurement data for flow depths above the centroid of the orifice are not available. In this case, the model that includes the approach Froude number had an average error of 1.92%, while other model that does not include the approach Froude number had an average error of 2.24%. It was found that the proposed stage-discharge relationships were in an excellent agreement with the experimental results.     

Analysis of flow through lateral rectangular orifices in open channels

A side lateral orifice in open channel is hydraulic control structure widely used in hydraulic, irrigation and environmental engineering for diverting the flow from main channel to a secondary channel. In this paper, analytical relationships for the discharge through side orifice are developed accounting for the pressure distribution over the area of the orifice. The computed discharges using the proposed relationship are within ±5% of the observed values; however percentage error is more in case the discharge is computed using earlier equations.     

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.     

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.     

Pareto genetic design of group method of data handling type neural network for prediction discharge coefficient in rectangular side orifices

The powerful method of Group Method of Data Handling (GMDH) was used for estimating the discharge coefficient of a rectangular side orifice. First, the existing equations for calculating the discharge coefficient were studied making use of experimental results. On the first hand, the factors affecting the discharge coefficient were determined, then five models were constructed in order to analyze the sensitivity in achieving accuracy by using different parameters. The results, obtained using statistical indexes (MARE=0.021 and RMSE=0.017), showed that one model out of the five models, on estimation using the dimensionless parameters of the ratio of depth of flow in main channel to width of rectangular orifice (Y_m/L), Froude number (Fr), the ratio of sill height to width of rectangular orifice (W/L) and width of main channel to width of rectangular orifice (B/L), presented the best results.     

基于差压式孔板流量计的缩径管段流场数值研究

基于ANSYS-CFX商业模拟软件,对差压式孔板流量计的内部流场进行数值模拟研究。计算了关于孔板流量计流出系数的4个主要影响因素：流量、粘度、缩径孔厚度及截面比,得到了不同模拟工况下的内部流场变化规律,同时借助数值模拟探讨了孔板流量计的冲蚀问题。将数值模拟流出系数计算值与基本经验公式编程计算值进行对比验证,结果显示两者吻合度高,误差基本控制在5％以内。研究表明,数值模拟可作为一种孔板流量计设计及标定的辅助方法。     

Evaluation of flow characteristics in labyrinth weirs using response surface methodology

Labyrinth weirs can increase the flow discharge capacity for a specific head and width by increasing the weir length. This paper studies the flow behavior of labyrinth weirs using Flow-3D® software. The main goal is to evaluate the capability of the response surface methodology (RSM), especially central composite design (CCD), to describe the performance of labyrinth weirs. Traditional and RSM-CCD methodologies are applied using experimental data of previous researchers and numerical data of the present study, respectively. Results show that RSM-CCD can produce an acceptably accurate model for the discharge coefficient of labyrinth weirs with only a small fraction of the data required for the traditional model. In addition, the discharge coefficient of a labyrinth weir decreases by increasing head and decreasing sidewall angle due to the inflow contraction and nappe interference in inlet and outlet cycles, respectively. The discharge efficiency can be up to 4.5 times higher for a labyrinth weir compared to a linear weir. Finally, a new method is introduced for designing labyrinth weirs.     

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 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.     

Numerical analysis of discharge coefficients in aerostatic bearings with orifice-type restrictors

Determining film pressure by solving the Reynolds equation is more effective than conducting bearing experiments or computational fluid dynamics simulations. The Reynolds equation can be solved easily in a numerical model; however, the accuracy of each model is dominated by the orifice discharge coefficient. This study compared two orifice flow models in inherent orifice restrictors and investigated the influences of geometry and flow parameters on the discharge coefficient. The results indicate that both orifice flow models can be used in inherent orifice restrictors, and the discharge coefficient of orifice-type restrictors is sensitive to the orifice diameter and film thickness.     

Flow through lateral circular orifice under free and submerged flow conditions

Open channels, with flow diversion structures such as orifices, weirs and sluice gates; are prevalent in irrigation systems, both for conveying water from the source to the irrigated areas, and for distributing the water within the irrigated area. The present study was broadly aimed at to investigate the flow characteristics of sharp-crested side circular orifices under free and submerged flow conditions through analytical and experimental considerations. It was also intended to develop relationships for coefficient of discharge for orifices under free and submerged flow conditions. The computed discharges using developed relationships were within ±5% and ±10% of the observed ones for free and submerged orifices, respectively. Sensitivity analysis reveals that the discharge through side orifice is more sensitive to the low head above the center of the orifice. Various parameters affecting the jet angles have been identified and relevant parameters are used for proposing relationships for the jet angle under different flow conditions.     

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.     

Stage-discharge relationship for slide gates installed in partially full pipes

Sluice/slide gates are widely used for flow depth control and flow discharge measurements in open channels. The hydraulic behavior of the sluice gates located in the rectangular open channels is well documented in the literature. This study reports the results of an investigation conducted to establish the stage-discharge relationship for the sluice gates located in horizontal, circular open channels/pipes under free outflow conditions. Different stage-discharge models were proposed based on the Buckingham's theorem of dimensional analysis and orifice theory. A comprehensive series of laboratory experiments (729 runs) were performed to study the sluice gates located at the middle, and at the end of two circular pipes. Using the data collected from two circular open channels of nominal diameters 20 and 30 cm, the proposed models were calibrated. For the middle slide gates, the experimental results showed that the discharge prediction can be improved by introducing the Reynolds number. For the slide gates located at the middle of the channel, the best proposed model has an average error of 1.40% with a maximum error of 7.12%. For the slide gates located at the end of the channel, the Reynolds number has no significant effect and best proposed model has an average error of 2.47% with a maximum error of 6.59%. The results also showed that the flow discharge of the end slide gate (with unconfined free jet under gravity) is higher than the flow discharge of the middle slide gate for the same gate opening areas and upstream flow depths. The proposed sluice/slide gate for circular open channels offers a simple and reliable discharge measurement approach with acceptable accuracy.     

Experimental analysis of combined side weir-gate located on a straight channel

Flow measurement and control in open channel system for lateral flow is important to support the system management. The flow characteristics of combined side weir-gate are complicated due to changes in flow conditions along the side weir-gate section. Experimental investigation of the flow characteristics of both weir and sluice gates is crucial for predicting the flow through a combined side weir-gate structure. Although weir-gate structures are widely used for frontal flow in hydraulic structures, the same is not true for lateral flows. In this study, 650 laboratory tests were conducted to determine the flow characteristics of combined side weir-gate for subcritical flow, and the experimental results were analyzed to determine the effect of these characteristics and weir-gate geometry on discharge capacity. Interaction factor of combined side weir-gate is a function of the upstream Froude number, the ratio of gate opening to upstream flow depth, the ratio of distance between the top of the sluice gate and the weir crest to gate opening, the ratio of weir and gate length to upstream flow depth, and the ratio of weir and gate length to main channel width. Consequently, more discharge is passed through combined side weir-gate compared to side weir and sluice gates. The empirically derived equations for the discharge of combined side weir-gate show good compatibility with the experimental data.     

Experimental modeling of flumes with two semi-cylinder contractions (free and submerged flows)

In this study, the flow through a simple low-cost flume constructed using two semi-cylinder contractions on either side of a rectangular channel was experimentally investigated. In practice, these flumes may operate under free- or submerged-flow conditions depending on the downstream flow depth. To reliably estimate the flume discharge, free- and submerged-flow conditions should be accurately distinguished. At present, there is no equation to estimate the submergence threshold. This study investigates the possibilities of using these flumes under submerged-flow conditions. The discharge of the submerged flume may be calculated on the basis of the free-flow discharge equation. Thus, two new free-flow discharge equations were deduced: a general equation by considering the contraction ratio with an average error of 2.25%, and another one by neglecting it with an average error of 4.88%. Compared with the existing discharge equations, the proposed free-flow equations are the best ones. Under submerged-flow conditions, the submergence ratio affects the flow discharge. Using the measurements carried out in this study, the submergence threshold ratio and submerged-flow discharge were formulated and calibrated with the average errors of 2.96% and 3.80%, respectively. The equation to distinguish the free- and submerged-flow conditions was also deduced by equating the submerged- and free-flow discharge equations yielding a novel real solution.     

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.     

Discharge coefficient influence on the performance of aerostatic journal bearings

Aerostatic journal bearings need externally pressurized air. The discharge coefficient is usually assumed constant for sonic and subsonic flow conditions. However, some authors found that it is variable as a function of the pressure ratio, orifice throat discharge and supply pressures. The present study is a theoretical investigation of the discharge coefficient influence on the performance of aerostatic journal bearings. The Reynolds equation for compressible fluids is solved by the finite element method with triangular linear elements. For 0.5 eccentricity ratio, the bearing load carrying capacity difference is 0.5%, although the bearing total mass flow rate difference is 7.4%.