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Weir Flow Calculator: Rectangular, V-Notch, and Cipolletti Discharge

Calculate Open Channel Flow Using Francis Formula and Standard Weir Equations

Free weir flow calculator for water and wastewater operators, civil engineers, and environmental technicians. Select rectangular, V-notch, or Cipolletti weir type, enter crest length and head to calculate flow rate in CFS, GPM, and MGD. Uses the Francis formula Q = 3.33 x (L - 0.2nH) x H^1.5 with end contraction corrections and velocity of approach adjustment.

Weirs are the simplest flow measurement device in open channels. No moving parts, no electronics, no calibration drift. Measure the head over the crest, plug it into the equation, and you have the flow rate. The trick is measuring head at the right location (at least 4H upstream of the crest) and making sure the weir is free-flowing with the nappe ventilated underneath. This calculator handles all three common weir types and generates a rating table for quick field reference.

Pro Tip: V-notch weirs are best for low flows under 1 CFS because small head changes produce measurable flow changes. A 90-degree V-notch at 0.5 ft head gives about 0.88 CFS. At 0.1 ft head, it gives just 0.008 CFS. That sensitivity disappears with rectangular weirs at low head. If you need to measure flows from 0.01 to 5 CFS, use a V-notch. Above 5 CFS, switch to rectangular.

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Weir Flow Rate Calculator
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How It Works

  1. Select Weir Type

    Choose rectangular (suppressed or contracted), 90-degree or 60-degree V-notch, or Cipolletti (trapezoidal with 1:4 side slopes). Each type has a different discharge equation.

  2. Enter Weir Dimensions

    Input crest length L (for rectangular and Cipolletti) or notch angle (for V-notch). Enter head H measured at least 4H upstream of the crest to avoid drawdown effects.

  3. Calculate Flow Rate

    The calculator applies the appropriate equation. For Francis formula with end contractions: Q = 3.33 x (L - 0.2nH) x H^1.5. Results show CFS, GPM, and MGD.

  4. Review Rating Table

    A rating table shows flow at incremental head values for creating staff gauge readings. Velocity of approach correction is applied for high-velocity channels.

Built For

  • Water treatment plant operators measuring influent and effluent flow rates with installed weirs
  • Civil engineers designing flow measurement structures for stormwater management
  • Environmental technicians monitoring stream flow for discharge permit compliance
  • Irrigation districts measuring water delivery through canal diversion structures
  • Mining operations measuring water discharge from settling ponds
  • Wastewater operators creating rating tables for weir-based flow measurement stations
  • Hydrologists calibrating stream gauging stations with temporary weir installations

Features & Capabilities

Three Weir Types

Rectangular (Francis formula), V-notch (90 and 60 degree), and Cipolletti (trapezoidal). Covers all standard flow measurement weirs.

End Contraction Correction

Adjusts rectangular weir calculations for 0, 1, or 2 end contractions. Suppressed weirs (no contractions) use the full crest length.

Velocity of Approach

Applies correction when upstream channel velocity adds kinetic energy to the effective head. Important for narrow approach channels.

Rating Table Output

Generates a table of flow vs head at specified increments. Print and post at the weir site for quick field readings.

Multiple Flow Units

Results in CFS, GPM, MGD, and liters per second. No manual conversions needed.

PDF Export

Export flow calculations and rating table as a branded PDF for compliance records or field reference.

Assumptions

  • Weir is sharp-crested with a thin plate edge (less than 1/8 inch) per standard hydraulic measurement practice
  • Head (H) is measured at least 4H upstream of the weir crest to avoid drawdown effects near the crest
  • Nappe is fully ventilated (air flows freely beneath the overflow sheet) for free-flow conditions
  • Francis formula for rectangular weirs: Q = 3.33 x (L - 0.2nH) x H^1.5, with n = number of end contractions
  • V-notch weir uses the Kindsvater-Shen equation calibrated to the selected notch angle (90 or 60 degrees)
  • Approach channel velocity is low enough that velocity of approach correction is negligible unless the user enables it

Limitations

  • Standard weir equations are only valid for free-flow (non-submerged) conditions — downstream water must be below the crest level
  • Submerged weirs require a correction factor that significantly reduces accuracy and is not modeled here
  • Sediment accumulation upstream of the weir changes the approach channel geometry and invalidates the calibration
  • Weir crest must be level and free of nicks, dents, or biological growth — a damaged crest produces inaccurate readings
  • V-notch weirs lose accuracy at very high heads (above 2 feet) where the flow may not form a stable nappe
  • Does not model broad-crested weirs, compound weirs, or proportional (Sutro) weirs used in specialized applications
  • Rating table accuracy assumes the weir geometry does not change over time due to corrosion or structural settlement

References

  • USBR (U.S. Bureau of Reclamation) — Water Measurement Manual, 3rd Edition (weir equations and installation standards)
  • ISO 1438 — Hydrometry: Open Channel Flow Measurement Using Thin-Plate Weirs
  • ASTM D5242 — Standard Method for Open-Channel Flow Measurement of Water with Thin-Plate Weirs
  • AWWA Manual M33 — Flowmeters in Water Supply (weir-based flow measurement in water treatment)
  • Kindsvater & Carter — Discharge Coefficients for Rectangular and Triangular Weirs (USGS calibration data)
  • Bos, M.G. — Discharge Measurement Structures, 3rd Edition (ILRI Publication 20, comprehensive weir design reference)

Frequently Asked Questions

V-notch weirs are most accurate for low flows (under 1 CFS) because small head changes produce measurable flow changes. Rectangular weirs handle larger flows and are easier to build. Cipolletti weirs eliminate end contraction corrections. For very large flows, broad-crested weirs are used. Choice depends on expected flow range and accuracy needs.
Q = 3.33 x L x H^1.5 for sharp-crested rectangular weirs with suppressed end contractions. With end contractions, effective length reduces by 0.1H per contraction: L_eff = L - 0.2nH. Head H must be measured at least 4H upstream of the crest.
Head is the vertical distance from weir crest to upstream water surface. Measure far enough upstream (at least 4H) that drawdown near the weir does not affect the reading. Use a staff gauge, stilling well, or pressure transducer. Downstream water must be below the crest for free-flow conditions.
When upstream velocity is significant (above 1 ft/s), kinetic energy adds to the effective head. The correction adds V-squared/2g to measured head. For accurate measurement, the approach channel should be at least 8 times wider than the crest and velocity kept below 0.5 ft/s if possible.
When downstream water rises above the crest (submerged), standard free-flow equations no longer apply. Submerged weirs need a correction factor based on the submergence ratio. Accuracy decreases significantly. For reliable measurement, the weir should operate in free-flow with the nappe fully ventilated.
Disclaimer: Weir flow calculations assume standard sharp-crested weir geometry and free-flow conditions. Field installations must be properly constructed and maintained for accurate measurement. Verify flow data against permit requirements with your regulatory agency.

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