HomeCalculatorsPhysicsFluid MechanicsBroad-Crested Weir Calculator
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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Rectangular broad-crested weir Q=C_d (2/3)^{3/2} b √g H^{3/2}, + O3 mpmath tabulated Q.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Rectangular broad-crested weir Q=C_d (2/3)^{3/2} b √g H^{3/2}, + O3 mpmath tabulated Q.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, alias, awkward, custom-cd, invalid-domain) · Matrix
Deferred
Not thin-plate L, not submerged H2, not Manning, not orifice, not Parshall/sluice/ogee.
Numerical scope
O2: broad-crested weir vs a separate-module identity (≤2 ULP). Not thin-plate L, not Manning, not orifice, and not submerged H2. ≤2 ULP vs O3 applies only to the published tabulated broad-crested vectors. Not thin-plate L, not Manning, not orifice, and not submerged H2.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
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 · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Rectangular broad-crested weir Q=C_d (2/3)^{3/2} b √g H^{3/2}, + O3 mpmath tabulated Q.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision
2026-09-26.o2-o3 · 1/1 property · digest a2f11ae37c1c
Legacy regression
6/6 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
4/4 golden · 1/1 CVP boundary · 3/3 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
Sources
Evidence
1 legacy golden · legacy regression suite · 4/4 oracle-backed golden · 3/3 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

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

1

Enter crest width b

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

2

Enter head H or discharge Q

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

3

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.

ϟ

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
ϟ

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

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 · 6/6 tests · Production surface contract 6/6 · 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
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: Alternate Depth Calculator, Bernoulli Equation Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator, Critical Slope Calculator . Explore all Fluid Mechanics.

→ Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product. › → Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser. › → Cavitation Number Calculator Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²). › → Chezy Formula Calculator Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy. › → Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup. › → Concentric Reducer Calculator Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av. › → Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av. › → Critical Slope Calculator Compute rectangular critical bed slope Sc such that yn=yc using SI Manning at y=yc. Runs locally. Not Manning A,R; not normal-depth yn; not critical-depth yc as the product; not Chezy; not Q=Av. ›

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.