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Weir Flow Rate Calculator

Calculate flow rate over weirs using Francis, V-notch, broad-crested, Cipolletti, and ogee weir formulas. Supports velocity approach and end contraction corrections.

Hydraulics & Water Resources Hydraulic engineers, water resources engineers Commercial Intent: HIGH

Engineering Formulas

Rectangular Sharp-Crested (Francis)

Q = 1.84 ร— L ร— H^(3/2) (SI) Leff = L โˆ’ 0.1 ร— n ร— H (with end contractions) With approach: Q = 1.84 ร— L ร— ((H + hv)^(3/2) โˆ’ hv^(3/2))
Q: Flow rate (mยณ/s)
L: Crest width (m)
H: Head over weir (m)
n: Number of end contractions
hv: Velocity head (m)

V-Notch (Triangular)

Q = (8/15) ร— Cd ร— tan(ฮธ/2) ร— โˆš(2g) ร— H^(5/2) Standard 90ยฐ: Q = 1.38 ร— H^(5/2) (Cd = 0.60)
ฮธ: Notch angle (degrees)
Cd: Discharge coefficient
g: Gravity (9.81 m/sยฒ)

Broad-Crested

Q = Cd ร— L ร— H^(3/2) ร— โˆšg Typical Cd = 0.58โ€“0.65 depending on H/Lw ratio
L: Crest width (m)
Cd: Discharge coefficient (0.58โ€“0.65)

Cipolletti (Trapezoidal)

Q = 1.859 ร— L ร— H^(3/2) Side slopes 1:4 (H:V)
L: Crest width (m)

Ogee / Spillway

Q = Cd ร— L ร— H^(3/2) ร— โˆš(2g) Cd โ‰ˆ 0.75 at design head
Cd: Discharge coefficient (โ‰ˆ0.75)

Engineering Notes

Always verify weir is operating under free-flow conditions (downstream water level at least 0.1 m below crest).
For submerged weirs, apply Villemonte correction factor.
V-notch weirs are most accurate for H between 0.05 m and 0.5 m.
The Francis formula is empirical and works best for H between 0.03 m and 0.6 m.
Ogee spillway discharge coefficient varies with H/Hd ratio โ€” use 0.75 for design head.

Assumptions

โ€ข Steady, uniform flow conditions
โ€ข Free-flowing weir (not submerged)
โ€ข Sharp-crested weir assumes fully aerated nappe
โ€ข Broad-crested weir assumes critical flow over crest
โ€ข V-notch assumes fully contracted triangular section
โ€ข Ogee weir assumes design head operation

Common Mistakes

โœ• Using wrong formula for weir type
โœ• Forgetting to apply end contraction correction for rectangular weirs
โœ• Not checking if weir is submerged (downstream water level above crest)
โœ• Using incorrect units โ€” H must be in meters
โœ• Ignoring velocity of approach when H/P > 0.5

Frequently Asked Questions

What is a weir used for?

Weirs are used to measure flow rate in open channels, control water levels, and divert flow. They are common in irrigation, wastewater treatment, and hydrology.

What is the difference between sharp-crested and broad-crested weirs?

Sharp-crested weirs have a thin crest that causes flow to spring clear (nappe). Broad-crested weirs have a wide crest where flow becomes parallel to the crest. Sharp-crested are better for measurement; broad-crested are better for control.

What is a V-notch weir best for?

V-notch weirs are best for measuring low flow rates because the triangular opening provides greater sensitivity at low heads. Standard 90ยฐ notches are most common.

What are end contractions?

End contractions occur when the weir notch is narrower than the channel, causing flow convergence at the ends. Each contraction reduces effective crest length by 0.1ร—H.

When should velocity of approach be considered?

Velocity of approach should be considered when the channel velocity is significant (>0.5 m/s) or when the weir height is small relative to head (H/P > 0.5).

What is the Cipolletti weir?

Cipolletti is a trapezoidal weir with 1:4 side slopes designed to compensate for end contractions, so the standard Francis formula without contraction correction applies.

How does an ogee spillway work?

An ogee spillway is shaped to match the lower nappe of a sharp-crested weir, minimizing negative pressure. It is used in dam spillways for high-flow discharges.

What is the standard discharge coefficient for sharp-crested weirs?

Cd โ‰ˆ 0.62 for rectangular sharp-crested weirs under free-flow conditions. Values range from 0.58 to 0.65 depending on weir geometry and head.

References & Standards

ISO 1438USBRChow (1959)
ISO 1438
Hydrometry โ€” Open channel flow measurement using weirs and flumes
USBR
Water Measurement Manual โ€” weir discharge tables and coefficients
Chow (1959)
Open-Channel Hydraulics โ€” definitive reference on weir hydraulics

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