Rectangular Weir Equation Calculator 
Discharge, Head, and Design Calculations. Equations and Installation Guidelines 

Register to enable "Calculate" button. Rectangular weir topics: Introduction Equations Installation Guidelines and Equation Applicability Error Messages References Introduction USBR (1997) provides equations for a "standard" fully contracted rectangular weir and a "standard" suppressed weir. The U.S. Bureau of Reclamation has conducted many weir tests over several decades using weirs with particular dimensions  usually b's in 1 ft. increments up to about 10 ft. Therefore, any weir outside their tested dimensions is nonstandard, and their equations should not be used. To provide a single reliable, accurate method to model all rectangular weirs (suppressed, partially contracted, and fully contracted), the KindsvaterCarter equation (Kindsvater and Carter, 1959) was developed. It is considerably more complex than the USBR standard weir equations. However, USBR (1997) states that the KindsvaterCarter method is at least as accurate, if not more, than the standard weir equations for suppressed and fully contracted weirs. And further, the KindsvaterCarter equation reliably models partially contracted weirs. ISO (1980), ASTM (1993), and USBR (1993) all recommend using the KindsvaterCarter method for all rectangular weirs. Rectangular Weir Equation ISO (1980) provides a graph and equations for C_{e} vs. h/P for b/B=0, 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. To account for other b/B values, LMNO Engineering developed an equation for all b/B values. The LMNO Engineering curves are plotted below with the ISO curves, so you can see our goodness of fit. Likewise, ISO (1980) provides values of K_{b} for b/B=0, 0.2, 0.4, 0.6, 0.8, and 1.0, and LMNO Engineering fit an equation through the data to facilitate solving numerically for b. The LMNO Engineering fit is shown below with the ISO data. Our numerical solutions utilize a cubic solver routine. The computations are performed in double precision (the calculations on all of our web pages use double precision). Rectangular Weir Installation Guidelines and Equation Applicability
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Page It doesn't matter how thick the weir is except where water flows through the notch. The weir should be between 1 and 2 mm thick in the opening. If the bulk of the weir is thicker than 2 mm, the downstream edge of the opening can be chamfered at an angle greater than 45^{o} to achieve the desired thickness of the edges. You want to avoid having water cling to the downstream face of the weir. Water surface downstream of the weir should be at least 0.2 ft. (6 cm) below the weir crest (i.e. below the bottom of the opening) (USBR, 1993). Measured head (h) should be ≥ 0.03 m (1.2 inch). P is measured from the bottom of the upstream channel and should be ≥ 0.1 m (3.9 inch). The notch width (b) and channel width (B) should be ≥ 0.15 m (5.9 inch). 0 < b/B ≤ 1 and 0 < h/P ≤ 2.5. If b<B (i.e. contracted weir), then (Bb) ≥ 0.2 m (3.9 inch). Error Messages given by calculation
Top of Page "h must be ≥0.03 m", "P must be 0.1 to 10000 m", "h/P must be ≤2.5", "b must be ≥ 0.15 m", "B must be 0.15 to 10000 m", or "b/B must be ≤1". These are initial checks of user input. Though ISO (1980) does not place an upper limit on P or B, our calculation imposes limits of 10000 m for practicality. For actual weirs, P and B generally don't exceed several meters. "h will be <0.03 m", "h will be >2.5P", "b will be <0.15 m", or "b will be >B". Inputs are such that the computed parameter will be out of range. "Infeasible input". Inputs are such that the computed parameter will be out of range. References ISO (1980). International Organization of Standards. ISO 1438/11980(E). Water flow measurement in open channels using weirs and venturi flumes  Part 1: Thin plate weirs. 1980. Available from Global Engineering Documents at http://global.ihs.com Kindsvater, C. E. and R. W. Carter. 1959. Discharge characteristics of rectangular thinplate weirs. Transactions, American Society of Civil Engineers. v. 24. Paper No. 3001. USBR (1997). U.S. Department of the Interior, Bureau of Reclamation. Water Measurement Manual. 1997. 3ed. Available from http://www.usbr.gov/tsc/techreferences/mands/wmm/index.htm .
© 19992024 LMNO Engineering, Research, and Software, Ltd. (All Rights Reserved) Please contact us for consulting or questions about weirs and flow measurement. LMNO Engineering, Research, and Software, Ltd.  To: LMNO Engineering home page (more calculations) Related calculations: End Depth Method: Circular Flumes: 