Open Channel Flow Measurement 5: the Rectangular Weir

A sharp crested, rectangular weir is simply a flat plate obstruction in an open channel flow path, with a straight, level opening to allow water flow over the weir, as shown in the pictures and diagrams in the rest of this article. It is used to meter flow of water over the weir (and through the open channel) by measuring the head of water over the weir crest. An introduction to the rectangular weir and several other types of weirs and flumes for measuring open channel flow rate is given in the first article of this series, "Open Channel Flow Measurement 1: Introduction to the Weir and Flume."

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Q = 3.33 B H^3/2, where Q is the water flow rate in ft³/sec, B is the length of the weir (and the channel width) in ft, and H is the head over the weir in ft.

Use of this equation is subject to the condition that H/P < 0.33 and H/B < 0.33.

Note from the diagrams above that P is the height of the weir crest above the bottom of the channel, and B is the channel width.

For S.I. units the suppressed rectangular weir equation becomes Q = 1.84 B H^3/2, where Q is the water flow rate in m³/sec, B is the length of the weir (and the channel width) in m, and H is the head over the weir in m. The same condition for H/P and H/B apply.

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Q = 3.33(L - 0.2H)H^3/2, where Q is the water flow rate in ft³/sec and H is the head over the weir in ft.

Use of this fully contracted rectangular weir equation is subject to the conditions that H/L < 0.33, B - L > 4 H_max, and P > 2H_max. L is the weir length, H_max is the maximum head over the weir, and H, B, & P are as identified above.

For S.I units the fully contracted rectangular weir equation is: Q = 1.84(L - 0.2H)H^3/2, where Q is the water flow rate in m³/sec, and H is in m. This weir equation is subject to the same conditions given above.

Problem: Consider a contracted rectangular weir in a rectangular channel with B = 6 ft, L = 2.4 ft, P = 1.2 ft, and H = 0.5 ft. Show that the conditions for use of the fully contracted rectangular weir equation are met and calculate the water flow rate for the 0.5 ft head over the weir.

Solution: Check on conditions: H/L = 0.5/2.4 = 0.21 -- OK; B - L = 6 - 2.4 = 3.6 & 4H = 2,

so B - L > 4H -- OK; P = 1.2 ft & 2H = 1 ft, so P > 2H -- OK.

Now calculate Q: Q = 3.33(2.4 - 0.2*0.5)0.5^3/2 = 2.708 cfs

The article, "Excel Templates for Rectangular Weir Calculations," has Excel spreadsheet templates for making both suppressed and contracted rectangular weir calculations available for download.

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:

Suppressed Rectangular Weir: U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual.

Contracted Rectangular Weir: Food and Agricultural Organization of the United Nations. http://www.fao.org/docrep/R4082E/r4082e06.htm

Rectangular, Sharp-Crested Weir: flowmeterdirectory.co.uk