Verified calculation capability

Chezy formula Calculation Capability

Open-channel Chezy V=C √(R S). C is Chezy C, not Manning n, not Hazen–Williams pipe C. Not Q=Av, not Darcy. · Physics · Fluid

Capability ID physics.fluid.chezy · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Mean velocity

Mean velocity: V = C √(R S)
Chezy C: C = V / √(R S)
Hydraulic radius: R = V² / (C² S)

Solve modes: velocity · C · R · S

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`C`	Chezy C. Required except C invert. Alternative: C_chezy.	—	input / output
`R`	Hydraulic radius in m. Required except R invert.	—	input / output
`S`	Friction slope. Required except S invert. Alternative: slope, Sf.	—	input / output
`v`	Mean velocity in m/s. Required for C, R, and S invert. Alternative: v_m_s. Do not send with velocity.	—	input / output
`v`	Mean velocity in m/s (query/UI). REST may send v.	m/s	input
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Uniform open-channel flow; V = C √(R S)
C is Chezy C, not Manning n, not Hazen–Williams pipe C
Not Q=Av, not Darcy, not a weir, not Manning

Not supported

Manning n
Q=Av identities
Hazen–Williams pipe C
Darcy–Weisbach
weirs
compound channels

Example

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

C=50 R=1 S=0.001 → V=50 √0.001

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: 17/17 calculation tests · golden 2/2 · boundary 10/10 · 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) @ 2026-09-17T09:03:11.906Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T09:03:11.074Z
Last production check: 2026-09-17T09:03:11.074Z
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: chezy-formula
Engine: chezy-formula
REST: POST /api/v1/calc/chezy-formula
MCP: execute_calculation with capability_id: "physics.fluid.chezy"
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 hydraulic radius
Chow, V.T. Open-Channel Hydraulics — Chezy formula

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.chezy"}}}'

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