Physics calculator

Broad-Crested Weir Calculator

Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Rectangular broad-crested weir discharge or head. Modular free nappe. Optional L_c and P envelopes.
Scope: Rectangular broad-crested weir: Q = C_d (2/3)^{3/2} b √g H^{3/2}; default C_d=0.85; modular free nappe; C_d is an input in (0, 1]
Verification: Engine tested · 5/5 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 3846 — Hydrometry — Open channel flow measurement using rectangular broad-crested weirs — Modular rectangular broad-crested weir
ISO 80000-4 — Mechanics — Volume flow rate
Bos, M.G. Discharge Measurement Structures — Broad-crested weirs
Sources
Evidence: 5 property · Production surface contract 1/1 · Artifact integrity PASS
Production: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T02:44:05.986Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

DischargeQ = C_d (2/3)^{3/2} b √g H^{3/2}

Head invertH = (Q / (C_d (2/3)^{3/2} b √g))^{2/3}

iSI g = 9.80665 m/s² unless given. Default C_d = 0.85. C_d must be in (0, 1]. Crest span is b, not thin-plate L. Do not send query v — that is calculation_version. yc=(2/3)H is reported, not an input.

How to use

Enter crest width b

Span across the channel. This is not thin-plate crest length L.

Enter head H or discharge Q

Give one, not both. H is upstream head above the crest, not energy head.

Optional C_d, L_c, P

Leave C_d blank for 0.85. REST may send streamwise L_c (ISO 3846 H/L_c in [0.08, 0.50]) or weir height P (H/P ≤ 1.5).

Example calculations

Common configurations with formula and result.

b=1 m, H=0.2 m

Default C_d=0.85, SI g

Q = 0.85 (2/3)^{3/2} (1) √g (0.2)^{3/2}

Q≈0.1296 m³/s

Invert H from that Q

b=1 m, Q≈0.1296 m³/s

H = (Q / (C_d (2/3)^{3/2} b √g))^{2/3}

H=0.2 m

Broad-Crested Weir calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 5/5 tests · Production surface contract 1/1
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Rectangular broad-crested weir. Modular free nappe. Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. H is upstream head above the crest, not energy head. Optional L_c envelope H/L_c∈[0.08,0.50]. Optional weir height P with H/P≤1.5. Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not Manning n, not Q=Av, not orifice C_d A √(2gH), not Francis 3.33.
What it calculates: Rectangular broad-crested weir discharge or head. Modular free nappe. Optional L_c and P envelopes.
Inputs: mode?
b
H | Q
Cd?
g?
L_c?
P?
Outputs: Q
H
b
Cd
g
yc
L_c?
P?
mode
model
Formula: Q = C_d (2/3)^{3/2} b √g H^{3/2}
Assumptions: Rectangular broad-crested weir: Q = C_d (2/3)^{3/2} b √g H^{3/2}; default C_d=0.85; modular free nappe; C_d is an input in (0, 1]
H is upstream head above the crest, not energy head; optional L_c envelope H/L_c∈[0.08,0.50]; optional P with H/P≤1.5
Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not Manning n, not Q=Av, not orifice C_d A √(2gH), not Francis 3.33 L H^{3/2}
Units: SI; b, H, L_c, P in m; Q in m³/s; g in m/s²
Boundary conditions: missing b, H, or Q when required → MISSING_REQUIRED_INPUT
H and Q together, thin-plate L, Manning n/R/S, orifice A/d/D/Δp, Q=Av v, yc/q/Fr, drowned h2 → MIXED_INPUT_ENCODING
C_d > 1, H/L_c outside [0.08,0.50] when L_c is given, or H/P > 1.5 when P is given → VALUE_OUT_OF_RANGE
mode=rectangular|triangular|thin-plate or unknown mode → MIXED_INPUT_ENCODING or INVALID_MODE
Example: b=1 H=0.2 → Q≈0.1296
Validation cases: 4 published on this page · 5/5 tests · Production surface contract 1/1 · View evidence
b=1 H=0.2 → Q = 0.85 (2/3)^{3/2} b √g H^{3/2} ≈ 0.1296
b=1 H=0.2 L=1 → MIXED_INPUT_ENCODING
b=1 H=0.2 Cd=3.33 → VALUE_OUT_OF_RANGE
mode=rectangular b=1 H=0.2 → MIXED_INPUT_ENCODING
Sources: ISO 3846 — Hydrometry — Open channel flow measurement using rectangular broad-crested weirs — Modular rectangular broad-crested weir
Supports: Q = C_d (2/3)^{3/2} b √g H^{3/2}; modular H/L_c range
ISO 80000-4 — Mechanics — Volume flow rate
Supports: Q is volume flow; H and b are lengths
Bos, M.G. Discharge Measurement Structures — Broad-crested weirs
Supports: Critical-flow rectangular broad-crested discharge; C_d of order 0.85
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute rectangular broad-crested weir discharge from crest width and upstream head.

Supported and not supported

Supported — modular rectangular broad-crested Q from b and H · invert H from Q · optional L_c and P envelopes · API physics.fluid.broad_crested_weir

Not supported — thin-plate (2/3) C_d L √(2g) H^{3/2}, V-notch, Manning n, Q=Av, orifice C_d A √(2gH), Francis 3.33, Kindsvater–Carter, Cipolletti, drowned nappe, critical-depth as a product page

Agent / API notes

Capability id: physics.fluid.broad_crested_weir · tool id: broad-crested-weir · pin 1.0.0.

{ "b": 1, "H": 0.2 }

Invert: { "mode": "head", "b": 1, "Q": 0.1296 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/broad-crested-weir. There is no /calc/fluid.

Other calculators in this family: Thin-plate weir, Manning formula, Critical depth, Flow rate, Parshall flume, Cutthroat flume .

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Frequently asked questions

Key distinctions behind the calculation.

Is this a thin-plate weir?

No. Thin-plate rectangular/V-notch Q=(2/3) C_d L √(2g) H^{3/2} is /calc/physics/weir-discharge (default C_d=0.62). Sending L or kind=rectangular here is MIXED_INPUT_ENCODING. At b=1 m and H=0.2 m this page reports Q≈0.1296 m³/s, not ≈0.1638 m³/s.

Is this a Parshall flume?

No. USBR 1–8 ft Parshall Q from throat W and gage Ha is /calc/physics/parshall-flume. Sending kind=parshall or W+Ha here is MIXED_INPUT_ENCODING.

Is this a cutthroat flume?

No. Skogerboe cutthroat Q from W, independent L_f, and Ha is /calc/physics/cutthroat-flume. Sending kind=cutthroat here is MIXED_INPUT_ENCODING.

Is this an ogee spillway?

No. USBR high-overflow ogee Q from L, H, and design head Hd is /calc/physics/ogee-spillway. Sending kind=ogee here is MIXED_INPUT_ENCODING.

Is this a side weir?

No. Borghei 1999 lateral overflow from B, y1, p, and Q1 is /calc/physics/side-weir. Sending kind=side here is MIXED_INPUT_ENCODING.

Is this the Manning formula?

No. Manning is uniform open-channel flow from n, A, R, and S at /calc/physics/manning-formula. Sending n, R, or S is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending A or v is MIXED_INPUT_ENCODING.

Is this an orifice?

No. A hole under head or a pipe orifice plate is /calc/physics/orifice-discharge. Sending A, d, D, or Δp is MIXED_INPUT_ENCODING.

Can I send Francis 3.33?

No. C_d must be in (0, 1]. Cd=3.33 is VALUE_OUT_OF_RANGE. Kindsvater–Carter contractions and Cipolletti are out of scope.

Is this the critical-depth page?

No. yc=(q²/g)^{1/3} as a product is /calc/physics/critical-depth. This page may report yc=(2/3)H. Sending yc, q, or Fr is MIXED_INPUT_ENCODING.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine broadCrestedWeir wrapper.