Weir Flow Calculator
Calculate open channel flow rates using weir measurements. This calculator supports rectangular, V-notch, and Cipolletti weir types for accurate discharge estimation in hydraulic engineering.
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Weir flow resultHow It Works
The Weir Flow Calculator uses established hydraulic formulas to determine the volumetric flow rate (discharge) over a weir based on the weir geometry and the measured head of water above the weir crest.
Rectangular Weir (Francis Formula)
The discharge over a rectangular weir is calculated using the Francis formula:
Q = 1.84 × (L - 0.1nH) × H^(3/2) (SI units, m³/s)
Where:
- • Q = Discharge (m³/s)
- • L = Weir crest length (m)
- • n = Number of end contractions (0, 1, or 2)
- • H = Head over weir (m)
V-Notch Weir (Thomson Formula)
The discharge over a V-notch (triangular) weir is calculated using:
Q = (8/15) × Cd × tan(θ/2) × √(2g) × H^(5/2)
Where:
- • Q = Discharge (m³/s)
- • Cd = Discharge coefficient (≈ 0.58)
- • θ = Notch angle
- • g = Gravitational acceleration (9.81 m/s²)
- • H = Head over weir (m)
Cipolletti Weir
The Cipolletti (trapezoidal) weir uses a simplified formula that accounts for end contractions through its sloped sides:
Q = 1.859 × L × H^(3/2) (SI units, m³/s)
Where:
- • Q = Discharge (m³/s)
- • L = Weir crest length (m)
- • H = Head over weir (m)
FAQ
Here you will find the answers to the frequently asked questions about weir flow calculations.
Frequently Asked Questions
What is a weir and how is it used to measure flow?
A weir is a barrier placed across an open channel that forces water to flow over it. By measuring the height (head) of water above the weir crest, the flow rate can be calculated using established hydraulic formulas. Weirs are widely used in irrigation, wastewater treatment, and environmental monitoring due to their simplicity and reliability.
When should I use a V-notch weir vs a rectangular weir?
V-notch weirs are ideal for measuring low flow rates because the narrow angle concentrates the flow, providing greater sensitivity and accuracy at small heads. Rectangular weirs are better suited for higher flow rates and wider channels. As a general rule, use a V-notch weir for flows below 30 L/s and a rectangular weir for larger flows.
What are end contractions and how do they affect flow?
End contractions occur when the weir crest is narrower than the channel, causing the flow to contract horizontally as it passes over the weir. Each contraction reduces the effective crest length, lowering the calculated discharge. The Francis formula accounts for this by subtracting 0.1nH from the crest length, where n is the number of contractions (0, 1, or 2).
How accurate is weir flow measurement?
Under ideal conditions, weir flow measurement accuracy is typically within 2-5%. Accuracy depends on proper installation, adequate upstream pool depth, a clean and sharp crest, accurate head measurement taken upstream of the drawdown zone, and ensuring the nappe (overflow sheet) is fully ventilated. Field conditions may reduce accuracy to 5-10%.
What is the minimum head required for accurate weir measurement?
For reliable results, the minimum head over the weir should be at least 50 mm (2 inches) for rectangular and Cipolletti weirs, and at least 60 mm (2.5 inches) for V-notch weirs. Below these thresholds, surface tension effects become significant and the standard discharge equations lose accuracy. The head should also not exceed one-third of the weir height for best results.
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