Rectangular Weir Calculator
Discharge, Head, and Design Calculations. Equations and Installation Guidelines
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Rectangular weir topics: Introduction Equations Installation Guidelines and Equation Applicability Error Messages References
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 non-standard, 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 Kindsvater-Carter equation (Kindsvater and Carter, 1959) was developed. It is considerably more complex than the USBR standard weir equations. However, USBR (1997) states that the Kindsvater-Carter method is at least as accurate, if not more, than the standard weir equations for suppressed and fully contracted weirs. And further, the Kindsvater-Carter equation reliably models partially contracted weirs. ISO (1980), ASTM (1993), and USBR (1993) all recommend using the Kindsvater-Carter method for all rectangular weirs.
Rectangular Weir Equation
ISO (1980) provides a graph and equations for Ce 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 Kb 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
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 45o 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 (B-b) ≥ 0.2 m (3.9 inch).
Error Messages given by calculation
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"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.
ISO (1980). International Organization of Standards. ISO 1438/1-1980(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 thin-plate 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 .
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