## Rectangular Weir Calculation Background

The Excel templates in this article will calculate the water flow rate over a rectangular weir based on input information about the weir and open channel geometry and the measured head over

the weir. The diagram at the left shows a longitudinal view of a sharp crested, rectangular weir with some of the parameters. The diagram at the right shows the difference between a suppressed rectangular weir (weir length = channel width) and a contracted rectangular weir (weir length < channel width).

The next two sections will present and discuss Excel templates that have the weir equations entered in as Excel formulas to make calculations for a suppressed rectangular weir and for a contracted rectangular weir.

For more background information about rectangular sharp crested weirs for measuring open channel flow rate, see the article, "Open Channel Flow Measurement 5: the Rectangular Weir."

## Suppressed Rectangular Weir Flow Calculator

The Excel template shown at the left will calculate the water flow rate over a suppressed rectangular weir. Three input values are needed: the height of the weir crest above the channel invert, P; the width of the channel, B (which is also equal to the weir length L); and the measured head over the weir, H. With these three input values, the Excel formulas will calculate H/P and H/B. If both of these are less than 0.33, then the equation, **Q = 3.33 B H**^{3/2}, can be used to calculate the weir flow, Q.

If either H/P or H/B is greater than 0.33, then the Kindvater-Carter equation should be used as follows:

**Q = (0.4000)(H/P) + 3.220)(L – 0.003)(H + 0.003)**^{3/2}.

The Excel spreadsheet template is set up to calculate Q using both equations. If H/P < 0.33 and H/B < 0.33, as in the example spreadsheet, then the two Q values will be nearly the same. If either H/P > 0.33 and/or H/B > 0.33, then there will be a greater difference between the two Q values and Q from the Kindsvater-Carter equation should be used.

Click here to download this Excel template.

## Contracted Rectangular Weir Flow Calculator

The first page of the Excel template for contracted rectangular weir flow calculations is shown at the left and a

second page is shown at the right. For a contracted rectangular weir, L < B, so in addition to the three input values needed for the suppressed rectangular weir (P, B, and H), a value for the weir length, L, must be entered.

The Excel formulas in this spreadsheet template will then calculate (B – L)/4H, P/H, and H/L. If (B -L)/4H and P/H are greater than 1 and H/L < 0.33, then the simpler equation, **Q = 3.33(L – 0.2H)H**^{3/2}, can be used.

If any of the three conditions are not met, then the equation to use is:

**Q = (C**_{1}**(H/P) + C**_{2}**)(L – 0.003)(H + k**_{b}**)**^{3/2}** **

If any of the three conditions are not met, you will need to use the value of L/B calculated by the spreadsheet, together with the graph and table on the second page, to obtain values for C_{1}, C_{2}, and k_{b}, and enter them in the indicated cells. The Excel formula built in the spreadsheet template will then calculate Q using the above equation.

Click here to download this Excel template.

## References and Image Credits

References for further information:

1. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, *Water Measurement Manual.*

2. Bengtson, Harlan H.,* Open Channel Flow III – Sharp Crested Weirs**, an online continuing education course for PDH credit.*

*3. Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.*

Images were all prepared by H. Bengtson