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DISCHARGE COEFFICIENT FOR SIDE COMPOUND WEIRS IN OPEN CHANNEL
Abstract
A side compound sharp crested weir is a flow diversion structure provided in one or both side walls of a channel to spill/divert water from the main channel Experimental programme for this study were conducted in Advance Hydraulic Laboratory of Department of Civil Engineering, Aligarh Muslim University, India. Dimensional analysis is carried out to estimate the functional relationship for the coefficient of discharge for
side compound weir. It is found that the coefficient of discharge depends on the approach flow Froude number, the ratio of the weighted crest height of the side weir to the length of the side weir and the ratio of the upstream depth in the channel to the length of side weir. On the basis of F-test, it is observed that P / Lis the most significant parameter for the prediction of Cd. The developed relationship using regression approach for the coefficient of discharge for side compound weir gives root means square error is 0.0634. The performance of the present model is based on the coefficient of correlation of the non-linear regression line between predicted values from the present model and desired output (R=0.8609), average percentage error (APE=-2.356), Absolute average deviation (AAD=13.406), Standard deviation (STDV=10.13) and scattering index (SI=0.1675).
... Given that in open channels, the most critical effective force is gravity, the effect of viscosity and surface tension can be ignored 5,55 , so Reynolds and Weber numbers can be removed from the above equation. ...
... In Eqs. (3) to (5), the values of this number are equal to 4.76%, 5.7%, and 3.65%, respectively. The mentioned results of the analysis of the cumulative frequency curve against the absolute percentage of error show the superiority of machine learning models over regression-based models. ...
In the present study, two kernel-based data-intelligence paradigms, namely, Gaussian Process Regression (GPR) and Kernel Extreme Learning Machine (KELM) along with Generalized Regression Neural Network (GRNN) and Response Surface Methodology (RSM), as the validated schemes, employed to precisely estimate the elliptical side orifice discharge coefficient in rectangular channels. A total of 588 laboratory data in various geometric and hydraulic conditions were used to develop the models. The discharge coefficient was considered as a function of five dimensionless hydraulically and geometrical variables. The results showed that the machine learning models used in this study had shown good performance compared to the regression-based relationships. Comparison between machine learning models showed that GPR (RMSE = 0.0081, R = 0.958, MAPE = 1.3242) and KELM (RMSE = 0.0082, R = 0.9564, MAPE = 1.3499) models provide higher accuracy. Base on the RSM model, a new practical equation was developed to predict the discharge coefficient. Also, the sensitivity analysis of the input parameters showed that the main channel width to orifice height ratio (B/b) has the most significant effect on determining the discharge coefficient. The leverage approach was applied to identify outlier data and applicability domain.
A side weir is a flow diversion device, which is widely used in irrigation as a head regulator of distributaries and escapes. This paper presents a concept for an elementary discharge coefficient that is related to the discharge flowing through an elementary strip along the side-weir length. Generalized equations for an elementary discharge coefficient for rectangular and triangular side weirs have been proposed. Experimental results show the accuracy of the proposed equations.
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.
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.
Side weirs are widely used in irrigation, land drainage, urban sewage systems, flood protection, and forebay pool of hydropower systems by flow diversion or intake devices. The hydraulic behavior of side weirs received considerable interest by many researchers. A large number of these studies are physical model tests of rectangular side weirs. However, in the study, Computational Fluid Dynamics (CFD) models together with laboratory models of labyrinth side weirs were used for determining the discharge capacity of the labyrinth side weir located on the straight channel. The discharges performances obtained from CFD analyses were compared with the observed results for various Froude number, dimensionless nappe height, dimensionless weir width, and weir included angle. The results obtained from both methods are in a good agreement.
Side weirs are one of the most common diversion structures used for flow control, irrigation, drainage networks, and waste-water channels. Side weirs are generally rectangular sharp crested in form and hence, have some limitations in precise flow measurement. For accurate flow measurement and management in wide range of discharges, use of compound side weirs are suggested in this study. Experiments have been carried out in a rectangular compound side weir with variable heights and widths. It was determined that discharge coefficient of a compound side weir is a function of upstream Froude number (Fr1), ratio of weighted crest height of weir to upstream water depth w̄/y1 and ratio of weir length to upstream water depth (L/y1). Based on the experimental data and regression modeling, a dimensionless equation has been developed for prediction of the discharge coefficient and an equation has been proposed for estimation of flow discharge in compound rectangular sharp crested side weirs. Through comparison of results of these equations and experimental data, good agreement was achieved. The mean and maximum relative errors of the discharge equation were -2.3% and 10.7%, respectively.
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.
Numerical investigations of flow over side weirs in rectangular and circular channels are reported. Numerical models are obtained from energy principles and solved by a finite difference method. The results are presented in graphic form. Theoretical and experimental equations are presented for the determination of the length of side weirs for rectangular and circular delivery channels. Comparative analyses of side-weir lengths computed for several example cases show that rectangular-channel side-weir procedures generally should not be used for design purposes or for obtaining approximate water-surface profiles along side weirs in a circular channel (except for the special case of a side-weir-height-to-channel-diameter ratio of P/D = 0.66). For all other ratios of P/D, the percent error incurred depends on the basic assumptions involved with the rectangular approximation procedure.
This paper describes the design and calibration of a compound sharp-crested weir consisting of two triangular parts with different notch angles. This weir provides accurate measurement for a wide range of flows without discontinuities. The lower triangular part of the weir handles the normal range of discharges at the measurement structure while the upper part measures the occasional higher peak flows. This weir will be installed on the crest of small concrete gravity dams for measuring runoff in experimental catchments. The weir was calibrated in the laboratory using a scaled model. Different geometries (combination of notch angles) were tested in order to validate the proposed theoretical discharge equations.
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 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.
Side weirs are commonly installed along the sides of open channels. Computation of water surface depth over side weirs is essential to determine their discharge. Analytical solutions for water surface profiles along a rectangular side weir are available only for triangular, rectangular and trapezoidal primary channels on the basis of constant specific energy. Given that circular channels are an important application in sewer systems, this research presents an elegant semianalytical solution (which involves incomplete elliptic integrals) for establishing the water surface profile along a rectangular side weir located in a circular. The solution is a useful computational tool for the evaluation and design of rectangular side weirs in open circular channels. DOI: 10.1061/(ASCE)IR.1943-4774.0000483. (C) 2012 American Society of Civil Engineers.
Side weirs are widely used for water level control in irrigation and drainage systems. These structures are also used to divert excess water from a main channel into a side channel. Computation of water surface profile along the side weir is essential to determine the discharge over the side weir. Estimation of discharge over the side weirs is still an important issue. Most previous research works for side weirs were carried out in channels with rectangular, trapezoidal and circular cross sections. An analytical solution for the water surface profile along a side weir is available in the technical literature only for the special case of a rectangular channel on the basis of a constant specific energy assumption (De Marchi’s water surface profile). No analytical solution is available for the case of triangular channel. This research presents an elegant analytical solution for establishing the water surface profile along a side weir in a triangular channel. The solution, which yields a direct computation of the flow profile, should be a useful tool for evaluation and design of side weirs in triangular channels.
Side orifices are widely used in irrigation and environmental engineering to spill or divert water from a channel. Flow characteristic of sharp-crested rectangular orifices under free flow condition in open channels is studied in the present paper. Existing discharge equations are checked for their accuracy using the data collected in the present study and available data in the literature and a new discharge equation has been proposed. The coefficient of discharge mainly depends on the approach flow Froude number and ratio of the size of orifice and bed width of the channel. Relationships for the coefficient of discharge, treating the orifice as large and small were developed. The computed discharges using these relationships were within ±5% of the observed ones. Measurement of three-dimensional velocities and visualisation of streamlines in a horizontal plane at the centerline of the orifice indicates that for the flow of low Froude number, almost all the streamlines divert towards the orifice. However, in the case of high Froude number flows, only those streamlines which are close to the side orifice are diverted towards the orifice. The opposite side of the boundary has significant effect on the diverted discharge of low Froude number compared to the flow of high Froude number. Circular orifice has been found to be more efficient compared to the rectangular orifice of the same opening area.
Side weirs are extensively used in the hydraulic and environmental engineering applications. The modeling of free surface flow over a labyrinth side weir is a sophisticated problem in the hydraulic engineering. The water surface profiles over the triangular labyrinth side weirs were investigated by many of the researchers experimentally and theoretically. In this study, the free surface flow over the triangular labyrinth side weir was modeled by using Volume of Fluids (VOF) method to describe the flow characteristics in subcritical flow conditions. A valid method, Grid Convergence Index (GCI) was used to determine the numerical uncertainty of the simulation results. The simulation results were compared with experimental observations, and good agreements were obtained between the both results.
Square Lateral orifices in open channel
- A S Ramamurthy
- S T Udoyara
- S Serraf
Ramamurthy, A.S., Udoyara, S.T., Serraf, S. Square Lateral orifices in open channel. Journal of
Environmental Engineering 135(5), 1986, 292-298.
- Irrig
- Drain
Irrig. Drain. Eng. 10.1061/(ASCE) IR.1943 4774.0000483: 2012b, 948-954.