Weir and Orifice Calculator

Sharp-crested weirs

Full width: Kindsvater-Carter, C_e = 0.602 + 0.075 H/P, with Rehbock as a check. With end contractions: Francis, Q = 3.33(L − 0.1NH)H^1.5. V-notch: Q = C_d(8/15)√(2g) tan(θ/2) H^2.5, and for 90° the USBR equation 2.49 H^2.48. Cipolletti: Q = 3.367 L H^1.5.

HEC-22 weir equation

Q = C_w √(2g) L H^1.5 with a dimensionless coefficient (HEC-22 4th ed. Eq. 10.32): about 0.37 for sharp-crested weirs, 0.415 with end contractions, 0.29–0.41 for broad-crested weirs. A riser crest is a weir with L = circumference.

Broad-crested weirs and embankments

Q = C L H^1.5 with the coefficient you enter (US units); values outside 2.4–3.4 are flagged.

Orifices and gates

A vertical opening is integrated over its wetted height, so an opening whose crown is above the water flows as a weir and a deep opening tends to C_dA√(2gh). A horizontal opening (riser top, grate) uses C_dA√(2gH). Sluice gate in free flow: Q = C_d b a √(2gH₁).

Submergence and ranges

Sharp-crested weirs only — Villemonte (1947): Q_s = Q_free(1 − (H₂/H)ⁿ)^0.385, n = 1.5 rectangular, Cipolletti and the HEC-22 form, 2.5 V-notch. A broad-crested weir or embankment with downstream water is refused with the reason (its submerged flow follows other curves: HEC-RAS, or HDS-5 roadway overtopping). The USBR Water Measurement Manual (Ch. 7 §15) puts the scatter of sharp-crested submergence corrections at about ±15 percent, so the corrected flow is shown as an estimate. Each method states when the head, height or coefficient is outside its published range.

The calculator is tested against the cases below every time its code changes.

Tolerance: discharge ±1% or half a unit of the last printed digit. HEC-22 uses g = 32.2 ft/s² (this calculator 32.174). HEC-22 Example 10.11 is not used because its printed table does not follow its own equations (details in the fixture file).

• Approach velocity head is not added (USBR Water Measurement Manual Ch. 7 §14 corrections), and heads are measured upstream of the drawdown. Kindsvater-Carter already carries the approach effect through H/P.
• Submergence is corrected for sharp-crested weirs only (Villemonte). A submerged broad-crested weir or embankment is not corrected here, and no published worked example of the Villemonte correction was found for the verification table: its cases are arithmetic checks of the equation.
• Roadway overtopping with a variable crest profile and multi-stage outlet structures are not combined; compute each opening and add the flows.
• Partial submergence of an orifice (tailwater between invert and crown) is not modelled; the free-discharge value is shown with a note.
• Coefficients depend on the structure as built. Your reviewing agency’s criteria decide which coefficients apply.

When does a weir stop flowing freely?

When the downstream water rises above the crest, the weir is submerged and the free-flow equation overstates the flow. For sharp-crested weirs, enter the downstream water level and the calculator applies the Villemonte correction, as an estimate. For a broad crest it refuses and points to HEC-RAS or HDS-5 roadway overtopping.

Which coefficient should I use?

Each device uses the coefficient of its published method, shown in How it works. For the HEC-22 weir equation you enter a dimensionless C_w (typical values are listed under the field); a value from your local criteria or a rating of the actual structure is better than a generic one.

How do I rate a riser pipe?

Compute its crest as a weir (crest length = circumference) and its top as a horizontal orifice, at the same head. At low heads the weir gives the smaller flow and governs; at higher heads the orifice does. The barrel below the riser can also limit the flow; check it separately.

Can I attach the calculation sheet to a design report?

You can print it and include it as a supporting calculation that you have checked. It is a calculation aid, not a sealed engineering document: the engineer of record reviews it and is responsible for the design, and the criteria of the reviewing agency decide which methods and values apply.