Verified calculation capability

Submerged weir Calculation Capability

Villemonte rectangular submerged weir: Qs=Qf [1−(H2/H1)^{1.5}]^{0.385} on thin-plate Qf. Not free-flow H only, not ogee Hd, not side weir B+Q1, not Manning n, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.submerged_weir · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Submerged discharge

Submerged discharge: Qs = Qf [1 − (H2/H1)^{1.5}]^{0.385}
Free-flow Qf: Qf = (2/3) C_d L √(2g) H1^{3/2}

Solve modes: flow · head

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`L`	Crest length in m. Required. Alternatives: L_m, crest. Not broad-crested b, not side-weir B.	—	input / output
`H1`	Upstream head above crest in m. Required. Alternatives: H_1, h1, upstream_head. Do not send free-flow H.	—	input / output
`H2`	Downstream head above crest in m. Required for flow. Alternatives: H_2, h2, downstream_head. Envelope H2/H1∈[0.20, 0.95]. Not ogee Hd, not Parshall Hb.	—	input / output
`Q`	Submerged discharge Qs in m³/s. Required for head. Alternatives: flow, Q_m3_s, Qs.	—	input / output
`Cd`	Thin-plate C_d for Qf. Optional; default 0.62. Must be ≤ 1. Alternatives: C_d, cd.	—	input / output
`Qf`	—	—	output
`s`	—	—	output
`g`	—	—	output
`n_exp`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Rectangular thin-plate; drowned nappe
SI g=9.80665 unless given
Villemonte n=1.5 and exponent 0.385; n is not Manning n
Default C_d=0.62; optional C_d in (0, 1]
Not free-flow H only, not ogee Hd, not side weir, not Manning, not Q=Av

Not supported

free-flow thin-plate H only
ogee Hd
side weir B+Q1
Manning n
Q=Av
V-notch

Example

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

L=1 H1=0.3 H2=0.15 → Qs≈0.25428

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) @ 2026-09-18T13:56:15.885Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T13:56:15.080Z
Last production check: 2026-09-18T13:56:15.080Z
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: submerged-weir
Engine: submerged-weir
REST: POST /api/v1/calc/submerged-weir
MCP: execute_calculation with capability_id: "physics.fluid.submerged_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 thin-plate weirs
Villemonte, J.R. Submerged-weir discharge studies — Engineering News-Record 139(26), 1947
ISO 80000-4 — Mechanics — Volume flow rate

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.submerged_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.