Verified calculation capability

Trapezoidal specific force Calculation Capability

Trapezoid specific force M = Q²/(gA) + A ȳ on A=(b+z y)y with ȳ=y(3b+2zy)/(6(b+zy)). Not rectangular ȳ=y/2, not trapezoid sequent y2, not trapezoid specific energy E, not Manning n, not Q=Av.

Physics · Fluid Capability ID physics.fluid.trapezoid_specific_force version 1.0.0 STALE

Model

Specific force

Specific force: M = Q²/(g A) + A ȳ
Section: A = (b + z y) y
Centroid: ȳ = y (3b + 2 z y) / [6 (b + z y)]

Modes: force · depth

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Bottom width in m	—	input / output
`z`	Side slope run/rise	—	input / output
`Q`	Volume flow in m³/s	—	input / output
`y`	Depth in m	—	input / output
`M`	Specific force in m²	—	input / output
`g`	Gravity in m/s²	—	input / output
`branch`	Depth invert branch: omit or subcritical	—	input
`y_alt`	—	—	output
`yc`	—	—	output
`Mc`	—	—	output
`ybar`	—	—	output
`A`	—	—	output
`T`	—	—	output
`v`	—	—	output
`Fr`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Trapezoid specific force: M = Q²/(gA) + A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; M is m²; z>0 is run/rise
Unknown is M (force mode) or y (depth invert, subcritical y>yc by default); conjugate y_alt is reported; Fr is reported not an input
Not rectangular ȳ=y/2; not trapezoid sequent y2; not trapezoid specific energy E; not Manning n; not Q=Av

Not supported

rectangular ȳ=y/2
trapezoid sequent y2
trapezoid specific energy E
Manning n
Q=Av
z=0

Example

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

Q=2 b=2 z=1 y=1 → M≈1.46930

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: Capability production binding: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · Evidence changed after the last successful production attestation. Re-attestation required. · Public/cache ✓ · Origin ✓
Semantic contract: PASS
Evidence attested at: 2026-09-23T02:27:54.588Z
Last production check: 2026-09-23T02:27:54.588Z
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 2/2.

Calculate with POST /api/v1/calc/trapezoidal-specific-force. See REST docs.

Tool id: trapezoidal-specific-force
Engine: trapezoidal-specific-force
REST: POST /api/v1/calc/trapezoidal-specific-force
MCP: execute_calculation with capability_id: "physics.fluid.trapezoid_specific_force"
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 80000-4 — Mechanics — Volume flow rate and force
Chow, V.T. Open-Channel Hydraulics — Specific force in a trapezoidal section

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

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.trapezoid_specific_force"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.