V-Notch (Triangular) Weir Calculator
Discharge and Head Calculations, Equations, and Guidelines for water flow measurement in streams and channels.
Units in V-notch weir calculation: ft3=cubic foot, gal=US gallons, m3=cubic meter, mm=millimeter, s=second
Topics for V-notch weir: Introduction Equations Installation Guidelines and Equation Applicability Error Messages References
Triangular Weir (V-Notch Weir) Equations
Installation Guidelines and Equation Applicability
Top of Page
Head (h) should be measured at a distance of at least 4h upstream of the weir.
It doesn't matter how thick the weir is except where water flows over the weir through the "V." The weir should be between 0.03 and 0.08 inches (0.8 to 2 mm) thick in the V. If the bulk of the weir is thicker than 0.08 inch, the downstream edge of the V can be chamfered at an angle greater than 45o (60o is recommended) 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 bottom of the V to allow a free flowing waterfall.
Measured head (h) should be greater than 0.2 ft. (6 cm) due to potential measurement error at such small heads and the fact that the nappe (waterfall) may cling to the weir.
The equations have been developed for h<1.25 ft. (38 cm) and h/P<2.4.
The equations have been developed for fully contracted V-notch weirs which means h/B should be ≤ 0.2.
The average width of the approach channel (B) should be > 3 ft. (91 cm).
The bottom of the "V" should be at least 1.5 ft. (45 cm) above the bottom of the upstream channel.
If your weir does not achieve some of the above criteria, you may have a "partially contracted V-notch weir" where h/B needs only to be ≤ 0.4, the bottom of the "V" only needs to be 4 inch (10 cm) above the bottom of the upstream channel, the approach channel only needs to be 2 ft. (61 cm) wide, and h can be up to 2 ft. (61 cm) instead of 1.25 ft. (38 cm). Partially contracted weirs use a different graph for C which is a function of h/P and P/B and is only valid for a notch angle of 90o. In the graph (not shown - see USBR, 1997), C varies from 0.576 to 0.6; whereas, for a fully contracted 90o notch, C is 0.578 from our graph shown above. Our calculation does not account for partially contracted weirs, but for most practical purposes the difference in C is inconsequential.
Error Messages given by V-notch weir calculation
Top of Page
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
USBR. (1997). U.S. Department of the Interior, Bureau of Reclamation. Water Measurement Manual. 3ed. Available from http://www.usbr.gov/tsc/techreferences/mands/wmm/index.htm .
© 1999-2015 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
August 25, 2015: Made text fields show 8 significant figures rather than 16. Calculation still uses double precision internally.
LMNO Engineering home page (more calculations)