Verified calculation capability

Weir discharge Calculation Capability

Thin-plate weir discharge. Rectangular Q=(2/3) C_d L √(2g) H^{3/2}. Triangular Q=(8/15) C_d √(2g) tan(θ/2) H^{5/2}. Not Manning, not Q=Av, not Darcy, not an orifice, not Francis contractions. · Physics · Fluid

Capability ID physics.fluid.weir · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Rectangular

Rectangular: Q = (2/3) C_d L √(2g) H^{3/2}
Triangular / V-notch: Q = (8/15) C_d √(2g) tan(θ/2) H^{5/2}

Solve modes: rectangular · triangular

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`H`	Upstream head above the crest in m. Give H or Q, not both.	—	input / output
`Q`	Discharge in m³/s. Give H or Q, not both.	—	input / output
`L`	Crest length in m. Required for rectangular.	—	input / output
`theta_deg`	V-notch angle in degrees. Default 90. Alternative: theta_rad. Do not send both.	—	input / output
`theta_rad`	V-notch angle in radians. Alternative: theta_deg. Do not send both.	—	input
`Cd`	Discharge coefficient. Default 0.62 rectangular, 0.58 triangular. Francis 3.33 is out of scope.	—	input / output
`g`	Gravity in m/s². Default 9.80665.	—	input / output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Thin-plate weir; free nappe
SI g=9.80665 unless given
Rectangular: Q=(2/3) C_d L √(2g) H^{3/2}; not Francis contractions
Triangular: Q=(8/15) C_d √(2g) tan(θ/2) H^{5/2}
Not Manning, not Q=Av, not Darcy, not an orifice

Not supported

Manning
Q=Av identities
Darcy–Weisbach
orifice plates
Francis 3.33 L H^{3/2}
Kindsvater–Carter contractions
Cipolletti
submerged nappe

Example

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

L=1 H=0.2 → Q=(2/3)(0.62)(1)√(2g) H^{3/2}

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: 15/15 calculation tests · golden 1/1 · boundary 9/9 · 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; 163 CURRENT) @ 2026-09-17T03:09:03.307Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T03:09:02.494Z
Last production check: 2026-09-17T03:09:02.494Z
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. Reference Calculation Standard — Production surface contract 3/3.

Tool id: weir-discharge
Engine: weir-discharge
REST: POST /api/v1/calc/weir-discharge
MCP: execute_calculation with capability_id: "physics.fluid.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 1438 — Hydrometry — Open channel flow measurement using thin-plate weirs — Rectangular and triangular thin-plate weirs
ISO 80000-4 — Mechanics — Volume flow rate
Chow, V.T. Open-Channel Hydraulics — Sharp-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.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.