When is a broad-crested weir used?

Broad-crested weirs are used as flow-measurement devices and as overflow spillways for low dams. They're more robust than sharp-crested weirs but have a wider range of discharge coefficient depending on geometry.

How does broad-crested weir flow differ from sharp-crested?

Broad-crested weirs have a broad, flat crest (typically wider than 2H upstream). The flow approaches critical depth on the crest, simplifying analysis. Sharp-crested weirs use a thin plate where the nappe springs free.

What is critical depth on the crest?

For free overflow, depth on the crest equals critical depth: y_c = (q²/g)^(1/3) where q is discharge per unit width. The depth ratio y_c/H ≈ 2/3 for ideal broad-crested weir flow.

What's the difference between broad-crested and ogee spillways?

An ogee spillway has a curved crest matching the underside of the nappe over a sharp-crested weir at design head. It's more efficient (C ≈ 3.95) than a broad-crested weir (C ≈ 3.0) but more expensive to construct. Use broad-crested for low/medium dams, ogee for major spillways.

Does the calculator account for submergence?

No — this calculator assumes free overflow (atmospheric pressure beneath the falling nappe). If downstream water surface rises above ~60–70% of upstream head, apply a submergence reduction factor from USBR Water Measurement Manual Figure 7-13.

How long must the crest be to be 'broad'?

The transition from sharp-crested to broad-crested occurs at H/B ≈ 0.08, where B is crest length in the flow direction. Broad-crested behavior holds for 0.08 ≤ H/B ≤ 0.50. Beyond H/B = 0.50, the structure behaves more like a stepped or short-crested weir.

What's the head measurement convention?

H is the total head over the crest, including approach velocity head. For high-velocity approach: H = h + V₁²/(2g), where h is depth above crest. For most low-velocity reservoirs, V₁²/(2g) is negligible and H ≈ h.

Broad-Crested Weir Calculator — Spillway Flow

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.

Discharge coefficient table

Pick the C-value matching your spillway crest geometry. Approach velocity, head/crest-thickness ratio, and approach depth all influence C; the values below are typical design ranges.

Discharge coefficients C for broad-crested weirs and spillways (Q = C·L·H^3/2)
Crest type / configuration	C (US, ft^1/2/s)	C (SI, m^1/2/s)
Round-nosed broad crest, smooth	3.05	1.69
Round-nosed broad crest, with sloped upstream face	3.10	1.71
Square-nosed broad crest	2.65	1.46
Square-nosed with rounded upstream corner	2.85	1.57
Earth dam emergency spillway, vegetated	2.85	1.57
Earth spillway, mowed grass	3.00	1.66
Concrete ogee spillway, at design head	3.95	2.18
Concrete ogee spillway, low head (H/Hd < 0.5)	3.55	1.96
Concrete ogee spillway, high head (H/Hd > 1.5)	4.10	2.26
Compound (stepped) crest, smooth steps	2.55	1.41
Trapezoidal cross-section, riprap-lined	2.65	1.46

Source: USBR (1987), Design of Small Dams, 3rd ed., Chapter 9. ASCE (1995) Hydraulic Design of Spillways, ASCE Manual 79. Brater, King, Lindell & Wei (1996), Handbook of Hydraulics, Table 5-1.

Worked examples

Example 1 — 30-ft concrete spillway, design flood Q₁₀₀

Given: 30-ft long round-nosed broad-crested concrete spillway (C = 3.05), Q₁₀₀ = 450 cfs, no piers.

Find: Required head H over the crest.

Solve Q = C·L·H^3/2 for H: H = (Q / (C·L))^2/3

H = (450 / (3.05 · 30))^2/3 = (4.918)^2/3

H = 2.89 ft above crest

Example 2 — Earth dam emergency spillway, 100-ft wide, vegetated

Given: Vegetated earth emergency spillway, L = 100 ft, C = 2.85, design flood produces H = 1.5 ft over crest.

Find: Discharge Q.

Q = 2.85 · 100 · (1.5)^1.5 = 285 · 1.837

Q = 523 cfs

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 = L_net − 2(NK_p + K_a)H, where K_p and K_a 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.