Discharge Formula for Sharp-Crested Rectangular Weirs (original) (raw)
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Discharge Coefficient of Contracted Rectangular Sharp-Crested Weirs, an Experimental Study
Journal of Engineering
An experimental study is made here to investigate the discharge coefficient for contracted rectangular Sharp crested weirs. Three Models are used, each with different weir width to flume width ratios (0.333, 0.5, and 0.666). The experimental work is conducted in a standard flume with high-precision head and flow measuring devices. Results are used to find a dimensionless equation for the discharge coefficient variation with geometrical, flow, and fluid properties. These are the ratio of the total head to the weir height, the ratio of the contracted weir width to the flume width, the ratio of the total head to the contracted width, and Reynolds and Weber numbers. Results show that the relationship between the discharge coefficient and these variables is a non-linear power function with a determination coefficient of 0.97. The importance and normalized importance analysis show that 56.3 % of the discharge coefficient variation is explained by the head-to-contracted width of the weir r...
Discharge coefficient of a rectangular sharp-edged broad-crested weir
Journal of Hydrology and Hydromechanics, 2014
This paper is concerned with the determination of the relationship for the calculation of the discharge coefficient at free overflow over a rectangular sharp-edged broad-crested weir without lateral contraction. The determination was made on the basis of new measurement in a range of the relative thickness of the weir from 0.12 to 0.30 and newly in a large range of relative height of the weir extremely from 0.24 to 6.8 which greatly expands the application possibilities of low weirs. In addition, the effects of friction and surface tension on the value of the discharge coefficient were evaluated as well as the effect of the relative thickness of the weir. The new equation for discharge coefficient, expressed using the relative height of the weir, was subjected to verification made by an independent laboratory which confirmed its accuracy.
Calibration of Compound Broad Crested Weir For Measurement of Discharge Ms
2017
Experiments were carried out to know the suitability of different shapes of broad crested weirs to replace the conventional method of discharge measurement with the help of venturi-flume. Even the weir used for it, had an indepen0dent use as energy dissipater. A series of laboratory experiments were performed in order to investigate the effects of the lower weir crest and step height of a broad-crested weir of rectangular compound cross section on the values of discharge coefficient, the approach velocity and the modular limit. The dependence of the three values on model parameters was investigated and the quantities were compared with those of the broad crested weir models with rectangular cross section. KeywordsCo-efficient of Discharge, Calibration of Weir,Broad crested weir, Discharge measurement, DepthDischarge relationship.
Broad-Crested Weir as a Device for Measurement of Discharge
Weirs are overflow structures, which alter the discharge so that flow rate can be calculated, flood can be prevented, or even make a body of water more navigable. Measurements of discharge are known based on the surface profile of the water. For estimation of discharge over the weir, weir coefficient is required. In this report only the broad crested weir is focused on. Design and the analysis of this weir are shown in the report. It was found that the broad-crested weir is best for measuring discharge in small medium channels. Flow over a broad-crested weir is highly dependent on the weir's geometry, it's a useful hydraulic tool which enables engineers to control water height, velocity, and most importantly they can be used to calculate discharge. Hydraulic structures such as weirs, flumes, and pipes, may cause the flow upstream of the structure to rise above the normal flow depth this is a common property.
Discharge Characteristics of Weirs of Finite Crest Length
Journal of Hydraulic Engineering, 2009
This paper considers flow measurement in open channels with transverse weirs of finite crest length with sloping crests and upstream or downstream ramps-or both-for free flows. Using the broad-crested weir equation with a discharge coefficient as the basis and following the earlier studies of broad-crested weirs, robust correlations have been developed for the discharge coefficient by using the experimental results available in the literature. Effects of upstream and downstream ramps were studied by introducing the upstream and the downstream length scales, respectively. The proposed correlations of embankment weirs were compared with the head-discharge formulations of embankment weirs in the literature. Triangular (hump) weirs with either upstream or downstream ramps (or both) have also been considered. It was found that in triangular (hump) weirs, the discharge coefficient increases when the downstream slope increases, but it decreases when the upstream slope increases.
Triangular weirs are commonly used to measure discharge in open channel flow, representing an inexpensive, reliable methodology to monitor water allocation. In this work, a low-speed photographic technique was used to characterize the upper and lower nappe profiles of flow over fully aerated triangular weirs. A total of 112 experiments were performed covering a range of weir vertex angles (from 30°to 90°), crest elevations (8 or 10 cm), and discharges (0.01-7.82 l s −1 ). The experimental nappe profiles were mathematically modeled and combined with elements of free-vortex theory to derive a predictive equation for the weir discharge coefficient. Comparisons were established between measured C d , the proposed discharge coefficient equation, and discharge coefficient equations identified in the literature. The proposed equation predicts C d with a mean estimation error (MEE) of 0.001, a root-mean square error (RMSE) of 0.004, and an index of agreement (IA) of 0.984. In the experimental conditions of this study, this performance slightly improves that of the equation proposed by Greve in 1932, and showed the same absolute value of MEE but lower values of RMSE and IA.
Experimental Study of Discharge with Sharp-Crested Weirs
2020
In this study the water flow in an open channel over a sharp-crested weir is investigated experimentally. For this reason a series of laboratory experiments were performed in an open channel with a sharp-crested weir. The maximum head expected over the weir, the total upstream water height and the downstream water height of the impact in the constant bed of the open channel were measured. The discharge was measured using a tank put right after the open channel. In addition, the discharge and the upstream velocity were also calculated using already known equations. The main finding is that the relative error percentage for the majority of the experimental measurements is ± 4%, meaning that the calculation of the discharge with a sharp-crested weir gives very good results compared to the numerical results from known equations.
Head-Discharge Relationships for Rectangular Flat-Crested Slit Weir
2016
The rectangular weir is the most commonly used device in channel and laboratory for flow measurement due to its simplicity. The rectangular sharp-crested slit weir has been shown to be good at measuring small (< 0.005 m 3 /s) flow rates. In this study, the rectangular slit weir concept is extended to find the head-discharge relationship of water flows over a contracted rectangular flat-crested slit weir under free flow conditions. The head-discharge relationship is determined experimentally using a nine different weir heights with 10 mm weir width and 4 mm weir crest thickness at small discharges (< 0.00067 m 3 /s). The experimental data of actual and predicted discharge is verified by using a statistical analysis. A linear regression equation correlating the head-discharge relationship provides an accurate prediction of free flow discharge over the weir to yield results within 2.1% error of actual discharges and have a strong relationship. The presented head-discharge equatio...
Development of Parabolic Weirs for Simplified Discharge Measurement
Biosystems Engineering, 2007
Discharge equations of all existing sharp crested flow measurement weirs involve some fractions such as exponents of flow depth, which make manual calculations difficult. In the present research work, weirs with a simplified discharge equation were designed by manipulating the weir profile so that the flow depth exponent was a whole number. A parabolic weir profile gave the simplified discharge equation with two as the flow depth exponent. A relationship for obtaining the parabolic weir profile with any weir angle was developed. The theoretical discharge of flow across the parabolic weir was derived using a geometric constant based on the weir profile. Four parabolic weirs with 301, 451, 601, and 901 weir angles were developed and evaluated in laboratory hydraulic flume. The flow regime across weirs was turbulent and the average coefficient of discharge was estimated as 0Á5570Á05. Weir angle specific discharge models (coefficient of determination R 2 X0Á986) were developed based on two approaches; the first based on the product of geometric constant and the mean coefficient of discharge, and the second on a non-linear regression model constant. Weir constant linear regression prediction equations (R 2 X0Á993), capable of predicting discharge characteristics in combination with discharge models at any intermediate weir angle, were fitted. Parabolic weirs have the merits of both rectangular and triangular weirs, and may find application in field irrigation, industrial flow, and automated control systems measurements.
Discharge formula based on brink depth over sharp-crested weirs
water supply, 2024
Weirs are among the most essential hydraulic structures for measuring water discharge in open channels. The prediction of water discharge over weirs should be as precise and straightforward measured as feasible. The experimental investigation of flow prediction over varied heights of a conventional rectangular sharp-crested weir was conducted in the present work. The investigation evaluated five ratios of weir height to length, P/b, of 0.33, 0.4, 0.47, 0.53, and 0.6, different water discharges, Q, of up to 17.25 L/s, and different bed slopes, S, between 0.001 and 0.01. The experiment’s findings reveal that a change in the bed slope has no significant effect on the brink depth, hb, for a constant water discharge. However, it influences the head over the weir, h, which is usually measured upstream of the weir location and used to predict water discharge. A simple, accurate formula was developed for predicting water discharge over rectangular sharpcrested weirs depending on the brink depth with mean absolute percent error (MAPE) and root-mean-square error (RMSE) of 1.714% and 0.229, respectively. In addition to having a simple form, the developed formula performs well, is unaffected by the bed slope, and applies to a wide range of h/P values, from 0.158 to 0.945.