Verified calculation capability

Broad-crested weir Calculation Capability

Rectangular broad-crested weir Q=C_d (2/3)^{3/2} b √g H^{3/2}, default C_d=0.85. Not thin-plate weir, not Manning, not Q=Av, not orifice, not Francis 3.33. · Physics · Fluid

Capability ID physics.fluid.broad_crested_weir · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Discharge

Discharge: Q = C_d (2/3)^{3/2} b √g H^{3/2}
Head invert: H = (Q / (C_d (2/3)^{3/2} b √g))^{2/3}

Solve modes: flow · head

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`b`	Crest span in m. Required. Alternatives: width, b_m, crest_width. Do not send thin-plate L or crest.	—	input / output
`H`	Upstream head above the crest in m. Required for flow. Alternatives: head, H_m. Not energy head.	—	input / output
`Q`	Volume flow in m³/s. Required for head invert. Alternatives: flow, Q_m3_s.	—	input / output
`Cd`	Discharge coefficient in (0, 1]. Optional, default 0.85. Alternatives: C_d, cd. Not Francis 3.33.	—	input / output
`g`	Gravity in m/s². Optional, default 9.80665. Alternative: g_m_s2.	—	input / output
`L_c`	Streamwise crest length in m. Optional ISO 3846 envelope H/L_c in [0.08, 0.50]. Alternatives: Lc, L_crest, crest_length. Not thin-plate L.	—	input / output
`P`	Weir height in m. Optional envelope H/P ≤ 1.5. Alternatives: P_m, weir_height. Not Manning wetted perimeter.	—	input / output
`yc`	—	—	output
`model`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

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}

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

Example

One numerical check. The calculator page holds worked steps and FAQ.

b=1 H=0.2 → Q≈0.1296

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 5/5 calculation tests · golden 0/0 · boundary 0/0 · property 5/5
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

Production attestation: 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
Evidence attested at: 2026-09-18T02:44:05.231Z
Last production check: 2026-09-18T02:44:05.231Z
Public / cache: PASS
Origin: PASS

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Production surface contract 1/1.

Tool id: broad-crested-weir
Engine: broad-crested-weir
REST: POST /api/v1/calc/broad-crested-weir
MCP: execute_calculation with capability_id: "physics.fluid.broad_crested_weir"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

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

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"physics.fluid.broad_crested_weir"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.