Discharge formula for rectangular sharp-crested weirs

Sharp-crested rectangular weirs used for discharge measurement in channels and laboratories are experimentally investigated. Height and width of weir plate are the two parameters characterizing the head-discharge relationship. Laboratory experiments are conducted by measuring the discharge and the head over the weir for variable weir heights and widths. Applicability of various formulations for the discharge coefficient are investigated. Experiments indicate that discharge is independent of weir height, when the weir is operated within an appropriate discharge range. Average velocity over the weir plotted against the weir head displays universal characteristics such that it can be used in the expression of discharge over the weir, eliminating the need for a discharge coefficient. The head-discharge relationship for a rectangular weir has distinct features for the partially contracted weirs and for the fully contracted slit weirs.     

Discharge characteristics of orifice spillway under oblique approach flow

Orifice type spillways are provided in the dam at lower level for facilitation in flushing of the sediment from the reservoir in addition to spilling the flood water. However, in most of the hydraulic structures, particularly in the earthen and rockfill dams, the spillway is not a part of the dam and it is provided on either of the banks of the river which results in oblique approach flow to the spillway that likely to affect the discharging capacity of the spillway. Presented in this paper is an experimental study for discharge characteristics of orifice type spillway under straight and oblique approach flow. Analysis of data indicates that discharge through the spillway decreases with increase of obliquity of the flow. The effect of the obliquity has been quantified and discharge equations for one, two and three simultaneous opening of the bays have been proposed.     

Free overall in circular channels with flat base: a method of open channel flow measurement

A free overfall at the end of an open channel offers a simple means of measuring flow discharge. In this paper, two methods are presented for the computation of end-depth and discharge of a free overfall from smooth circular channels with flat base. Firstly, applying the momentum equation based on the Boussinesq approximation, the flow upstream of a free overfall is theoretically analyzed to calculate the end-depth-ratio (EDR). This approach eliminates the need of an experimentally determined pressure coefficient. In subcritical flows, the EDR is related to the critical-depth that occurs far upstream. In supercritical flows, the Manning equation is used to express the end-depth as a function of streamwise slope of the channel. Methods to estimate discharge from the end-depth in subcritical and supercritical flows are presented. The upstream flow profiles of a free overfall are computed using the streamline curvature at free surface. Secondly, an alternate method for analyzing free overfall from circular channels with flat base is also presented, where a free overfall in a circular channel with flat base is simulated by the flow over a sharp-crested weir to calculate the EDR. The comparisons of the computed results with the experimental data are satisfactory for subcritical flow and acceptable for supercritical flow.     

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.     

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.     

Free overall in open channels: state-of-the-art review

Seventy years ago, Hunter Rouse observed that a free overfall in rectangular channels could be used as a simple flow measuring device that requires no calibration. Due to its practical importance, since then many investigators studied the free overfall in various channels. Although the laboratory experimental results are rather simple, the mathematical treatments of free overfall problems have been found to be deceptively complicated. This article presents a comprehensive state-of-the-art review of the important laboratory experimental and theoretical investigations on free overfall in various channels highlighting the hydraulic background and the mathematical treatment of the problem. In this review article, 120 references are included.     

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.     

Application of LSPIV to measure supercritical flow in steep channels with low relative submergence

Measuring flow discharge has always been one of the most important concerns of water experts. To measure discharge in streams using velocity-area method it is necessary to quantify average velocity of the flow. It is not feasible to measure velocity by contact approaches like current meters under certain conditions such as in flood periods or for very shallow flows. Flow surface image velocimetry methods as non-intrusive solutions have recently been widely utilized to measure discharge in open channels. One of these methods is a variety of PIV method named LSPIV which has been very popular due to the elimination of laser application. In this study, LSPIV was used to measure 2D velocity field over the surface of steep supercritical flow. The obtained surface velocity data were used to calculate Velocity Index (VI) which is multiplied by surface velocity to convert it to mean velocity and subsequently flow discharge. Also, a few relations were proposed to calculate the VI according to the slope and relative submergence. Since, Velocity Index has been so far mostly studied for subcritical conditions, results of this study may be applied for measuring supercritical flows. Eventually, the proposed method was verified to be used for discharge measurement and was proven quite precise in this regard.     

Free overfalls in flat-based circular and U-shaped channels

This paper presents a theoretical model based on the free vortex theorem that is capable of predicting the pressure head distribution at the brink of free overfalls in open channels. This approach is coupled with the momentum equations to obtain the end-depth-ratio (EDR) from which the discharge can be estimated. In order to illustrate its flexibility, the theory is successfully applied to flat-based circular and U-shaped channels. Using previous experimental data, the proposed method is validated.     

Counter-current air-water flow in narrow rectangular channels with offset strip fins

Counter-current two-phase flows of air-water in narrow rectangular channels with offset-strip fins have been experimentally investigated in a 760 mm long and 100 mm wide test section with 3.0 and 5.0 mm gap widths. The two-phase flow regime, channel-average void fractions and two-phase pressure gradients were studied. Flow regime transition occurred at lower superficial velocities of air than in the channels without fins. In the bubbly and slug flow regimes, elongated bubbles rose along the subchannel formed by fins without lateral movement. The critical void fraction for the bubbly-to-slug transition was about 0.14 for the 3 mm gap channel and 0.2 for the 5 mm gap channel, respectively. Channel-average void fractions in the channels with fins were almost the same as those in the channels without fins. Void fractions increased as the gap width increased, especially at high superficial velocity of air. The presence of fins enhanced the two-phase distribution parameter significantly in the slug How, where the effect of gap width was almost negligible. Superficial velocity of air dominated the two-phase pressure gradients. Liquid superficial velocity and channel gap width has only a minor effect on the pressure gradients.     

A new approach to improve the discharging capacity of sharp-crested triangular plan form weirs

Conventional weirs are inherited with afflux and submergence of area upstream of the weir. Various weirs of modified plan form have been suggested in the past to enhance their discharging capacity and to restrict the afflux. Presented in this paper are results of the experimental study carried out to investigate the discharging capacity of a sharp-crested triangular plan form weir under free flow conditions in a rectangular channel. The efficiency of the triangular plan form weirs is better than the normal weir and also high for low vertex angle and decreases with the increase of ratio of head over the crest of the weir and crest height due to interference of the water jets downstream. The computed discharge using the proposed equation is within ±5% of the observed ones. Sensitivity of the weir, i.e., change of discharge due to unit change in head is also carried out which indicates that the weir is more sensitive at the low head and low vertex angle.     

A neural network approach for prediction of discharge in straight compound open channel flow

Most natural rivers and streams consist of two stage channels known as main channel and flood plains. Accurate prediction of discharge in compound open channels is extremely important from river engineering point of view. It helps the practitioners to provide essential information regarding flood mitigation, construction of hydraulic structures and prediction of sediment load so as to plan for effective preventive measures. Discharge determination models such as the single channel method (SCM), the divided channel method (DCM), the coherence method (COHM) and the exchange discharge method (EDM) are widely used; however, they are insufficient to predict discharge accurately. Therefore, an attempt has been made in this work to predict the total discharge in compound channels with an artificial neural network (ANN) and compare with the above models. The mean absolute percentage error with artificial neural networks is found to be consistently low as compared to other models.     

Weir velocity formulation for sharp-crested rectangular weirs

Discharge in open channels can be measured by sharp-crested rectangular weirs. Generally, measured head over the weir crest is substituted into an empirical formula derived from energy considerations to calculate the discharge. Assumptions made on the derivation are taken into account by defining a discharge coefficient that fits into the experimental data. In this study, a physical quantity, the average velocity over the weir section defined as ‘weir velocity’ is directly formulated as function of weir geometry and head over the weir. Weir velocity plotted against the weir head has a universal behavior for constant weir width to channel width ratio independent of the weir size. This unique behavior is described in terms of weir parameters to calculate the discharge without involving a discharge coefficient. Combining weir velocity data for variable weir widths provides a basis for direct formulation of discharge. The weir velocity exhibits simpler functional dependency on weir parameters in contrast to the discharge coefficient.     

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.     

Effect of the downstream transition region of a flow measurement flume of rectangular compound cross section on flow properties

In this study, the effect of the downstream expansion region of a flow measurement flume of rectangular compound cross section on some of the flow properties; such as the discharge coefficient, C_d, the approach velocity coefficient, C_v and the modular limit, ML were investigated. For this reason, extensive laboratory tests were conducted with nine models of different downstream transitions. The aforementioned hydraulic quantities were then related with the relevant parameters to obtain sets of curves from which one could decide which kind of downstream transition type would produce the highest modular limit. It was found that model type A yielded the highest modular limit with a downstream slope of about 1/7.     

Application of video imagery techniques for low cost measurement of water surface velocity in open channels

Developments in digital video recording technology make the video imagery tools more popular for velocity measurement in water flows. This has especially been of large interest due to its inherent advantage of non-contact nature which is quite handy in extreme flow conditions. Particle Image Velocimetry (PIV), Particle Tracking Velocimetry (PTV) and Large Scale Particle Tracking Velocimetry (LSPTV) are applied to free surface channel flow for water surface velocity measurement. Experiments are conducted to measure either a single point velocity applying PTV or velocity profiles across the channel width applying PIV on the water surface in a rectang typical velocities of nearly 1 andular tilting flume for various flow conditions. Technical issues regarding tracer particle size and type, travel distance, lighting, recording speed, camera position, image distortion and state of flow are discussed. Measured data is compared to computational results obtained from a numerical model involving a non-linear turbulence model capable of predicting turbulence driven secondary flows. Confirmation of reasonable match between computational and experimental results whereby applying mutual collaboration of them for discharge measurement has been attested. In addition to discharge, boundary roughness has also been predicted as an outcome of the numerical solution.     

Time resolved measurement of pulsating flow using orifices

This article reviews the theoretical background of the measurement of pulsating flow using orifices as flow to pressure transducers, providing a synopsis of work done in this field. Special attention is paid to the temporal inertia and the applicability of expressions thereof given in the literature. Other factors influencing the measurement, such as changing flow profiles and the effect of connection tubes between the pressure sensor and the orifice are discussed. An experiment was performed to investigate the applicability of an equation taking reverse flow and temporal inertia into account for the measurement of pulsating flow with relative pulsation amplitudes around 1 and frequencies up to 50 Hz. It was found that the suggested equation may give tolerable results if the ratio of the pulsating part of the velocity to the angular frequency times orifice diameter is not too high. For high ratios, however, the results could not be explained by the suggested equation.     

Multiphase flow measurements using coupled slotted orifice plate and swirl flow meter

Multiphase flow metering is a major focus for oil and gas industries. The performance of a modified version of a close coupled slotted orifice plate and swirl flow meter for multiphase flow was evaluated to provide further development of a new type of multiphase flow meter. The slotted orifice provides well homogenized flow for several pipe diameters downstream of the plate. This characteristic provides a homogeneous mixture at the inlet of the swirl meter for a wide range of gas volume fractions (GVF) and flow rates. In order to evaluate the performance of the designed flow-meter, its response was investigated for varying pressures and water flow rates. The proper correlations were established to provide high accurate two-phase flow measurements. The new proposed approach provides the GVF measurement with less than ±0.63% uncertainty for GVF range from 60% to 95%.     

Experimental study of discharge formulas for rectangular sharp-crested weirs under free flow condition

Laboratory experiments were carried out to investigate the discharge characteristics of rectangular sharp-crested weirs under free flow condition. The performances of available discharge formulas have been evaluated by using the experimental data sets of present and previous studies. Error statistics of our experimental data indicate that the recent stage-discharge relationships show satisfactory performances. Discharge formula in terms of weir Reynolds number proposed by Vatankhah gives the highest accuracy among the existing slit weir equations, with $E_{\pm 4}=100.00\text{\%}$ (i.e. percent error less than or equal to $\pm 4$) and a mean absolute error ${\left|E\right|}_m=0.88\text{\%}$. The full-range discharge equation presented by Bijankhan and Mahdavi Mazdeh shows the highest accuracy among the relationships in terms of weir contraction ratio, with $E_{\pm 4}=100.00\text{\%}$, ${\left|E\right|}_m=0.91\text{\%}$ for slit weirs and, $E_{\pm 4}=94.64\text{\%}$, ${\left|E\right|}_m=1.60\text{\%}$ for partially contracted weirs, respectively. The weir velocity formulae suggested by Gharahjeh et al. exhibit the relatively better performance, with $E_{\pm 4}=98.41\text{\%}$, ${\left|E\right|}_m=1.34\text{\%}$ for slit weirs and, $E_{\pm 4}=91.07\text{\%}$, ${\left|E\right|}_m=1.91\text{\%}$ for contracted weirs, respectively. Statistical results of this study confirm the weir velocity approach presented by Aydin et al. and show that, the weir velocity is a predominant quantity for rectangular sharp-crested weirs, unique characteristics of the weir velocity curves make it more suitable for expressing the discharges. Moreover, it is important to point out that the performance of weir velocity formulae can be further improved.     

Hydraulic characteristics and flow measurement performance analysis of portable fish-shaped flumes in U-shaped channels

Achieving accurate flow measurement in small channels is important to improve water use efficiency and reduce agricultural water waste. Commonly used fixed flumes have the disadvantages of high construction cost and easily causing local deposition in channels resulting in large measurement errors. There are no such disadvantages fixed type flumes in portable measuring flumes. However, portable flume types are less commonly used, and have not been widely applied. In this study, a streamlined portable fish-shaped cylinder (the plane figure is fish-shaped) was designed for flow measurement based on bionics and critical flow measurement principles. Prototype and numerical simulation experiments were conducted to study the hydraulic characteristics of the fish-shaped flume in U-shaped channels, which were under conditions of different discharges, slopes and contraction ratios. The hydraulic characteristics and flow measurement performance of the portable fish-shaped flume in the U-shaped channels were analyzed. The results showed that the numerical simulation results based on the RNG k-ε three-dimensional turbulence model were in good agreement with the prototype experiment. This study demonstrates that the proposed portable fish-shaped flumes can be used for flow measurement in small channels with the advantages of high measurement accuracy, high portability, small head loss, small upstream turbulence, and high submergence degree.