Weir Flow Calculator Formula
Understand the math behind the weir flow calculator. Each variable explained with a worked example.
Formulas Used
Flow Discharge (Q)
discharge = (2/3) * cd * weir_width * sqrt(2 * 9.81) * pow(head, 1.5)Flow Rate
discharge_lps = (2/3) * cd * weir_width * sqrt(2 * 9.81) * pow(head, 1.5) * 1000Variables
| Variable | Description | Default |
|---|---|---|
cd | Discharge Coefficient (Cd) | 0.62 |
weir_width | Weir Width (b)(m) | 2 |
head | Head above Weir Crest (H)(m) | 0.3 |
How It Works
Rectangular Weir Flow
A weir is a barrier across a channel over which water flows. The flow rate relates to the upstream head.
Formula
Q = (2/3) Cd b sqrt(2g) H^(3/2)
where Cd is the discharge coefficient, b is the weir width, g = 9.81 m/s^2, and H is the head (water depth above the crest measured upstream). This formula applies to rectangular, full-width (suppressed) weirs.
Worked Example
A 2 m wide suppressed weir with 0.3 m head, Cd = 0.62.
- 01sqrt(2 x 9.81) = sqrt(19.62) = 4.429
- 02H^(3/2) = 0.3^1.5 = 0.1643
- 03Q = (2/3) x 0.62 x 2 x 4.429 x 0.1643
- 04Q = 0.4133 x 4.429 x 0.1643 = 0.601 m^3/s = 601 L/s
Frequently Asked Questions
Where do I measure the head?
Measure the head (H) upstream of the weir at a distance of at least 3-4 times the maximum head. This avoids the drawdown effect near the crest.
What is a contracted vs suppressed weir?
A suppressed weir spans the full channel width. A contracted weir is narrower, so the flow contracts at the sides. For contracted weirs, reduce the effective width: b_eff = b - 0.1nH, where n is the number of contractions.
Can I use this for a V-notch weir?
No. V-notch (triangular) weirs use a different formula: Q = (8/15) Cd sqrt(2g) tan(theta/2) H^(5/2). V-notch weirs are more accurate for low flow rates.
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