What's a sharp-crested weir?

A thin vertical plate with a sharp upstream edge that creates a free-falling overflow. Used to measure flow in open channels and as the standard reference for weir flow theory. Discharge coefficient C is well-characterized empirically.

When does sharp-crested weir flow apply?

When the head H above the crest is at least 0.05 ft (15 mm) above the crest — below that, surface tension affects the nappe. Also requires the nappe to ventilate freely (atmospheric below the falling sheet).

What's the typical discharge coefficient?

C = 3.33 (US units, ft^0.5/s) or C = 1.84 (SI, m^0.5/s) is the Francis coefficient for sharp-crested rectangular weirs. For contracted weirs (crest narrower than channel), use the Francis formula with end-contraction correction: effective length L_eff = L − 0.1·n·H, where n is the number of end contractions.

How accurate is a sharp-crested weir for flow measurement?

With proper installation (vertical plate, sharp crest, free nappe ventilation, head measurement at 4H upstream), accuracy is ±2–3% of true discharge over the calibrated range (typically 0.05 ft ≤ H ≤ 2 ft for sharp-crested rectangular).

What is the H/P ratio limit?

For accurate measurement, H/P should be ≤ 0.4, where H is head over the crest and P is the weir height (crest above channel bottom). At higher H/P, the approach velocity head becomes significant and the basic equation under-predicts discharge by 5–15%.

When should I use a V-notch weir instead?

V-notch weirs are more accurate for low flows because the head H rises faster per unit discharge change. Use a V-notch when expected flow varies over a wide range or when minimum flow is small (< 0.1 cfs). Use rectangular sharp-crested for steady moderate-to-high flows.

Can sharp-crested weirs be used for spillways?

Sharp-crested weirs are flow-measurement devices, not structural spillways. For spillway design use a broad-crested or ogee weir profile, which has a higher discharge coefficient (~3.97 for ogee, vs 3.33 for sharp-crested) and is structurally robust.

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Sharp-Crested Rectangular Weir Calculator

Discharge over a thin-plate rectangular weir from crest length and upstream head. Used for flow measurement in ditches, lab flumes, and small treatment-plant outflow structures.

Units

Weir type

Crest length, Lft

Upstream head, Hft

Discharge coefficient, C— (US: ft½/s)

Effective length, L_e—ft

Discharge, Q—cfs

Default C = 3.33 in US units (≈ 1.84 in SI) is the Francis coefficient for sharp-crested weirs.

Suppressed weir (no end contractions):

$$ Q = C \, L \, H^{3/2} $$

Contracted weir (Francis correction for two end contractions):

$$ Q = C \, (L - 0.2 H) \, H^{3/2} $$

Q discharge · C discharge coefficient (≈ 3.33 ft½/s in US, 1.84 m½/s in SI) · L crest length · H head measured upstream of the weir.

When to use a sharp-crested weir

Sharp-crested weirs are accurate flow measurement devices for steady or slowly-varying flow in small to medium channels — typical applications include irrigation ditch metering, water-treatment plant effluent measurement, laboratory flumes, and stream gauging in ungauged watersheds. Accuracy is ±2–3% with proper installation.

Installation requirements

Weir plate vertical, at right angles to flow.
Crest sharp (not rounded). Rounded crest = broad-crested weir; different equation.
Approach channel straight for at least 4× the channel width upstream.
Head H measured at a stilling well at least 4H upstream of the weir.
Free fall on the downstream side; nappe must be ventilated to atmospheric pressure or the weir becomes submerged and inaccurate.

Suppressed vs. contracted

A suppressed weir spans the full channel width — the channel walls suppress the end contractions of the nappe. A contracted weir is shorter than the channel width, allowing end contractions on both sides. The Francis equation reduces the effective length by 0.1H per end contraction (so 0.2H for two-sided contraction).

Range of applicability

The equation is valid for H/P ≤ 0.4, where P is the weir height (crest above channel bottom). For higher H/P, the approach velocity head becomes significant and the basic equation under-predicts discharge by 5–15%. For tall weirs (H/P → 0), accuracy is best.

Weir discharge coefficients — comparison

Different weir profiles have different discharge coefficients. Use this table to pick the right equation for the structure you actually have.

Discharge coefficients C for common weir types (US units, Q = C·L·H^3/2)
Weir type	C (US, ft^1/2/s)	C (SI, m^1/2/s)	Notes
Sharp-crested rectangular (Francis)	3.33	1.84	Standard reference
Sharp-crested, with approach velocity correction	3.27 + 0.4·H/P	1.78 + 0.22·H/P	Rehbock equation
Broad-crested, square corners	2.6–2.8	1.43–1.55	Rounded crest, see broad-crested page
Broad-crested, rounded upstream corner	3.0–3.1	1.66–1.71	Spillway profile
Ogee spillway (USBR standard)	3.97	2.19	At design head
Cipolletti weir (trapezoidal, 1H:4V sides)	3.367	1.86	Compensates for end contraction
V-notch (90°)	2.49·H^1/2	1.38·H^1/2	Q = C_v·H^5/2, low flow
Sutro (proportional) weir	varies	varies	Designed for linear Q-H

Source: Brater, King, Lindell & Wei (1996), Handbook of Hydraulics, 7th ed., Chapter 5. USBR (1997) Water Measurement Manual, Chapter 7.

Worked examples

Example 1 — Suppressed weir on a 4-ft channel

Given: 4-ft wide rectangular concrete channel, full-width sharp-crested weir at the outlet, head H = 0.6 ft.

Find: Discharge Q.

L = 4.0 ft (suppressed: L_eff = L)

Q = 3.33 · 4.0 · (0.6)^1.5 = 13.32 · 0.4648

Q = 6.19 cfs

Example 2 — Contracted weir for outflow measurement

Given: Rectangular weir, crest length L = 3.0 ft installed in a 6-ft wide channel (so 2 end contractions), head H = 0.8 ft.

Find: Discharge Q with Francis end-contraction correction.

L_eff = L − 0.1·n·H = 3.0 − 0.1·2·0.8 = 3.0 − 0.16 = 2.84 ft

Q = 3.33 · 2.84 · (0.8)^1.5 = 9.46 · 0.7155

Q = 6.77 cfs

Reference: USBR (1997). Water Measurement Manual (3rd ed.), Chapter 7. Original: Francis, J.B. (1855). Lowell Hydraulic Experiments. Also Brater & King's Handbook of Hydraulics, Chapter 5.

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