{
  "capability_id": "physics.fluid.chezy",
  "tool_id": "chezy-formula",
  "engine": "chezy-formula",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-17T08:49:50.937Z",
  "engine_build": "2026-09-17",
  "test_count": 17,
  "passed": 17,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 2,
      "passed": 2
    },
    "boundary": {
      "total": 10,
      "passed": 10
    },
    "property": {
      "total": 5,
      "passed": 5
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/physics/chezy-formula",
  "api": "https://www.calculatorx.com/api/v1/calc/chezy-formula",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.chezy.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.chezy.output.json",
  "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"
  ],
  "limitations": [
    "Open-channel Chezy: V = C √(R S); C is Chezy C, not Manning n, not Hazen–Williams C",
    "Uniform flow; R is hydraulic radius; S is friction slope",
    "Not Manning, not Q=Av, not Darcy, not Hazen–Williams, not a weir"
  ],
  "boundary_conditions": [
    "missing C, R, S, or v when required → MISSING_REQUIRED_INPUT",
    "C, R, S, or v ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "n, k, A, Q, D, L, hf, f, Re, ε, K, Kv, Cv, D1/D2, C_d → MIXED_INPUT_ENCODING",
    "manning, darcy, or hw as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Volume flow rate and hydraulic radius",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "Hydraulic radius R is a length; mean velocity is length per time",
      "kind": "standard"
    },
    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Chezy formula",
      "supports": "Uniform-flow Chezy V = C √(R S); Manning is a later roughness encoding of C",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:e7aca832e10de5dac46a613e4cad54d344e81ba3f3b56f66e111f9b7880fc4ba",
  "tests": [
    {
      "id": "golden-ch-v",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "C": 50,
        "R": 1,
        "S": 0.001
      },
      "expect": {
        "v": 1.5811388300841895,
        "C": 50,
        "R": 1,
        "S": 0.001,
        "mode": "velocity",
        "model": "chezy"
      },
      "expectWarning": null,
      "actual": {
        "mode": "velocity",
        "v": 1.5811388300841895,
        "C": 50,
        "R": 1,
        "S": 0.001,
        "model": "chezy"
      },
      "tol": 1e-12
    },
    {
      "id": "golden-ch-C",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "C",
        "v": 1.5811388300841895,
        "R": 1,
        "S": 0.001
      },
      "expect": {
        "C": 50,
        "model": "chezy"
      },
      "expectWarning": null,
      "actual": {
        "mode": "C",
        "v": 1.5811388300841895,
        "C": 50,
        "R": 1,
        "S": 0.001,
        "model": "chezy"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ch-R",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "R",
        "v": 1.5811388300841895,
        "C": 50,
        "S": 0.001
      },
      "expect": {
        "R": 1,
        "model": "chezy"
      },
      "expectWarning": null,
      "actual": {
        "mode": "R",
        "v": 1.5811388300841895,
        "C": 50,
        "R": 0.9999999999999998,
        "S": 0.001,
        "model": "chezy"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ch-S",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "S",
        "v": 1.5811388300841895,
        "C": 50,
        "R": 1
      },
      "expect": {
        "S": 0.001,
        "model": "chezy"
      },
      "expectWarning": null,
      "actual": {
        "mode": "S",
        "v": 1.5811388300841895,
        "C": 50,
        "R": 1,
        "S": 0.0009999999999999998,
        "model": "chezy"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ch-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "R": 1,
        "S": 0.001
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "C is required"
    },
    {
      "id": "boundary-ch-c0",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 0,
        "R": 1,
        "S": 0.001
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "C must be greater than zero"
    },
    {
      "id": "boundary-ch-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 50,
        "R": 1,
        "S": 0.001,
        "n": 0.013
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Chezy does not take Manning n. That is /calc/physics/manning-formula. Give Chezy C"
    },
    {
      "id": "boundary-ch-A",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 50,
        "R": 1,
        "S": 0.001,
        "A": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Chezy does not take Q=Av A/Q or Manning A/P. Give R. Q=Av is /calc/physics/flow-rate"
    },
    {
      "id": "boundary-ch-D",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 50,
        "R": 1,
        "S": 0.001,
        "D": 0.5
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Chezy does not take pipe D, L, or hf. That is Hazen–Williams or Darcy"
    },
    {
      "id": "boundary-ch-manning",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 50,
        "R": 1,
        "S": 0.001,
        "mode": "manning"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be velocity|C|R|S. Not Manning, Darcy, Hazen–Williams, or Q=Av"
    },
    {
      "id": "boundary-ch-K",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 50,
        "R": 1,
        "S": 0.001,
        "K": 0.5
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Chezy C is not minor-loss K, valve Kv/Cv, or orifice C_d"
    },
    {
      "id": "boundary-ch-f",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 50,
        "R": 1,
        "S": 0.001,
        "f": 0.02
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Chezy does not take Darcy f or Colebrook Re/ε"
    },
    {
      "id": "property-ch-v",
      "ok": true,
      "kind": "property",
      "detail": "V=C √(R S)",
      "expect": 1.5811388300841895,
      "actual": 1.5811388300841895
    },
    {
      "id": "property-ch-roundtrip-C",
      "ok": true,
      "kind": "property",
      "detail": "C invert",
      "expect": 50,
      "actual": 50
    },
    {
      "id": "property-ch-roundtrip-R",
      "ok": true,
      "kind": "property",
      "detail": "R invert",
      "expect": 1,
      "actual": 0.9999999999999998
    },
    {
      "id": "property-ch-roundtrip-S",
      "ok": true,
      "kind": "property",
      "detail": "S invert",
      "expect": 0.001,
      "actual": 0.0009999999999999998
    },
    {
      "id": "property-ch-model",
      "ok": true,
      "kind": "property",
      "detail": "chezy",
      "expect": true,
      "actual": "chezy"
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 17,
      "total": 17,
      "golden": 2,
      "boundary": 10,
      "property": 5
    },
    "contract_checks": {
      "passed": 3,
      "total": 3
    }
  },
  "evidence_core_generated_at": "2026-09-17T06:42:15.154Z",
  "rendered_at": "2026-09-17T08:49:50.937Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
      "engine": "1.0.0",
      "page": "1.0.0",
      "capability": "1.0.0",
      "evidence": "1.0.0",
      "input_schema": "1.0.0",
      "output_schema": "1.0.0",
      "mcp_contract": "1.0.0"
    },
    "digests": {
      "input_schema_sha256": "a6e6387fdc8ee3a14e970a5c7fc3d2f5ff2a30befa7ceda00dc9c4df67d82b85",
      "output_schema_sha256": "d4ba08efdb93225367c70ff8df5625dedd5542f87839814d7348c54a7d929fef",
      "evidence_sha256": "ac15d75351ca848dccb45a73ea330b650fb885df12b8c355673be23b93c6aa3b",
      "evidence_core_sha256": "ac15d75351ca848dccb45a73ea330b650fb885df12b8c355673be23b93c6aa3b",
      "capability_sha256": "f487eb0fd774d45f973307fbab7d847046eaef431dfe5b7f10d25117120ee7c0",
      "engine_sha256": "0c0851fab70abbeebfe07916fc4e23f4718babe41882681bdfec8e4f0768b97f",
      "mcp_contract_sha256": "e444fb05e9379f4f2492792d89493686e8dd71c0a104ae00acbe73364b370c5c"
    },
    "contract_checks": {
      "total": 3,
      "passed": 3,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}