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

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 selected simplified equation. For rectangular contracted flow, Q = 3.33 x (L - 0.2H) x H^1.5 for two end contractions. Results show CFS, GPM, and MGD.

4. Review Rating Table

   A rating table shows flow at incremental head values for field-review context. Velocity-of-approach, submergence, and standard-specific corrections remain outside the app.

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 preparing preliminary weir-flow screens before permit-method review
• 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 comparing temporary weir readings before accepted calibration or rating review

Features & Capabilities

Three Thin-Plate Weir Prompts

Rectangular (Francis-style), V-notch (90, 60, 45, or custom angle), and Cipolletti (trapezoidal) prompts for preliminary flow screening.

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 Gap

Flags that approach velocity can affect readings, but does not apply a velocity-of-approach correction. Use the applicable standard or accepted rating method when it matters.

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 project records or field reference. Permit/compliance flow reporting still requires the regulator-approved measurement method.

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 prompt uses local coefficients for 90, 60, and 45 degree notches or 2.5 x tan(theta/2) for custom angles
• Velocity-of-approach, submergence, and standard-specific corrections are not applied

Limitations

• Standard weir equations are only valid for free-flow (non-submerged) conditions - downstream water must be below the crest level
• Submerged weirs require standard-specific or regulator-approved correction/rating procedures 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 reliability assumes the weir geometry does not change over time due to corrosion, biological growth, debris, 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