Weir Flow Calculator
Enter measured geometry and head, your discharge coefficient, and gravity. This transparent screening calculation does not replace a calibrated rating or hydraulic design.
Sources: USGS triangular-notch weir characteristics; USBR Water Measurement Manual, weirs and broad-crested weirs. https://www.usgs.gov/publications/discharge-characteristics-triangular-notch-thin-plate-weirs · https://www.usbr.gov/tsc/techreferences/mands/wmm/chap07_03.html · https://usbr.gov/tsc/techreferences/mands/wmm/chap02_13.html
| Quantity | Value | Unit |
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A QUICK WALKTHROUGH
How to use this tool
- Choose one geometry and enter dimensions in metres.
- Enter head above the crest or the explicitly defined upstream-to-orifice-centre head, plus Cd and g.
- Calculate, review the assumptions, then copy or download the report. Editing any input clears the result.
Equations and head datum
Rectangular sharp crest: Q=Cd·(2/3)b√(2g)H^(3/2). V-notch: Q=Cd·(8/15)tan(θ/2)√(2g)H^(5/2). Broad crest: ideal critical-flow estimate Q=Cd·(2/3)^(3/2)b√g H^(3/2). Free orifice: Q=Cd·A√(2gH), where H is upstream free-surface elevation above the centre of the opening. H is measured vertically from the crest for weirs. All lengths and g are user supplied.
Limits
Assumes steady incompressible liquid, free discharge, and the selected idealized geometry. Not for submerged weirs/orifices, approach-velocity correction, side contractions, nonstandard crest profiles, aeration effects, or calibration. An orifice must discharge freely to atmosphere; submerged orifices are excluded unless the entered head is explicitly the differential head between two free surfaces, which this tool does not calculate. Check dimensions and coefficient against a suitable hydraulic reference.
Sources
Equation context: USGS, Discharge Characteristics of Triangular-Notch Thin-Plate Weirs (https://www.usgs.gov/publications/discharge-characteristics-triangular-notch-thin-plate-weirs); USBR Water Measurement Manual, Weir Nomenclature and Classification (https://www.usbr.gov/tsc/techreferences/mands/wmm/chap07_03.html) and Rectangular Broad-Crested Weirs (https://usbr.gov/tsc/techreferences/mands/wmm/chap02_13.html). These references describe broader calibrated methods and operating conditions; this page implements only the simplified equations stated above.
Local report
Calculations run in this browser. The editable comparison table and TXT report contain the input snapshot, converted values, formula and caveats. Editing any field clears the prior result.
GOOD TO KNOW
Common questions
What is H?
For all three weirs, H is the vertical water-surface height upstream above the crest. For an orifice, H is the upstream free surface above the opening centre; the jet must discharge freely to atmosphere.
Does this handle tailwater or submerged flow?
No. Submerged-flow corrections and differential-head calculations are outside scope.
Are Cd and gravity supplied for me?
No. Enter values appropriate to your installation. The tool does not recommend defaults.