Broad-Crested Weir Calculator
Discharge over a flat-topped weir or spillway crest where the crest is wide enough that the flow becomes critical at the crest. The standard equation for dam spillways, drop structures, and concrete overflow weirs.
Defaults: 20 ft long uncontrolled spillway, 2 ft of head, typical concrete crest.
Discharge coefficient values
- Round-nosed broad crest: C = 3.0 to 3.1 (1.66 to 1.71 SI)
- Square-nosed broad crest: C = 2.6 to 2.8 (1.44 to 1.55 SI)
- Concrete ogee spillway (design head): C = 3.95 to 4.04 (2.18 to 2.23 SI) — use the ogee-specific equation, not this calculator
- Earth dam emergency spillway, vegetated: C = 2.8 to 3.0 (1.55 to 1.66 SI)
Broad vs. sharp-crested distinction
A weir is "broad" when the crest length in the flow direction (the thickness of the weir) is enough for the flow to become critical (depth = critical depth) on top. The transition is roughly at H/B between 0.08 and 0.50, where B is crest thickness — below 0.08, the weir is sharp-crested; above 0.50, the weir behaves more like a step or short-crested structure.
Submergence
If the downstream water level rises above 60–70% of the upstream head over the crest, the weir becomes submerged and the discharge equation under-reads. Apply a submergence reduction factor — see USBR Water Measurement Manual figure 7-13 or Brater & King chapter 5. For dam-safety inflow design floods, the spillway is typically assumed not submerged at peak.
Effective crest length
The crest length L should be reduced for piers and abutments (contractions). For a spillway with two abutments and N piers, effective length = Lnet − 2(NKp + Ka)H, where Kp and Ka are pier and abutment contraction coefficients (~0.01–0.05 each). For preliminary calculations, ignore contraction; for spillway sizing, account for it.
Reference: USBR (1987). Design of Small Dams (3rd ed.), Chapter 9. Also Chow (1959) Open-Channel Hydraulics and ASCE Manual 51, Design of Hydraulic Structures.