{
  "capability_id": "physics.fluid.critical_depth",
  "tool_id": "critical-depth",
  "engine": "critical-depth",
  "calculation_version": "1.0.0",
  "generated_at": "2026-11-10T05:18:41.945Z",
  "engine_build": "2026-09-18",
  "test_count": 17,
  "passed": 17,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 2,
      "total": 2
    },
    "boundary": {
      "passed": 10,
      "total": 10
    },
    "property": {
      "passed": 5,
      "total": 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/critical-depth",
  "api": "https://www.calculatorx.com/api/v1/calc/critical-depth",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.critical_depth.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.critical_depth.output.json",
  "assumptions": [
    "Rectangular critical depth: yc = (q²/g)^{1/3}; q = Q/b; default g=9.80665 m/s²",
    "Critical speed vc = √(g yc) is reported, not an input; Fr=1 is the definition, not a Froude wrap",
    "Not a Froude wrap, not specific energy E, not a hydraulic jump, not Manning, not Q=Av"
  ],
  "limitations": [
    "Rectangular critical depth: yc = (q²/g)^{1/3}; q = Q/b; default g=9.80665 m/s²",
    "Critical speed vc = √(g yc) is reported, not an input; Fr=1 is the definition, not a Froude wrap",
    "Not a Froude wrap, not specific energy E, not a hydraulic jump, not Manning, not Q=Av"
  ],
  "boundary_conditions": [
    "missing q or yc when required → MISSING_REQUIRED_INPUT",
    "q, yc, Q, b, or g ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "Fr/L, E/y, y1/y2, n, A, v, z → MIXED_INPUT_ENCODING",
    "froude, energy, or jump as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Length, speed, acceleration",
      "supports": "yc is a length; q is discharge per width; g is acceleration",
      "kind": "standard"
    },
    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Critical flow",
      "supports": "yc = (q²/g)^{1/3} for a rectangular channel at Fr=1",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:649c7fa8bd29869eca9c3e854991a768943aa7b9146bc63b206422d3ee53e7e1",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 17,
      "total": 17,
      "golden": 2,
      "boundary": 10,
      "property": 5
    },
    "contract_checks": {
      "passed": 5,
      "total": 5
    }
  },
  "evidence_core_generated_at": "2026-09-18T22:05:44.918Z",
  "rendered_at": "2026-11-10T05:18:41.945Z",
  "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": "d49a2eacfe2366fc685869d86c01f1c37d7dd297fd06351f4d8e2465063279d7",
      "output_schema_sha256": "abecc9666596c2b02a611a9636356763de9935f68c5547102e1c88f40ad8703e",
      "evidence_sha256": "acdd687a6e1b20e68c4a022bf7fc863763b8617c6bcf09775510486312cd2596",
      "evidence_core_sha256": "acdd687a6e1b20e68c4a022bf7fc863763b8617c6bcf09775510486312cd2596",
      "capability_sha256": "057273bf6d8683ac923f965a98744312212bf4c171d2efff73f298f677dbd371",
      "engine_sha256": "c6ebd8436f08b413e1ac6317b2d48550f2e6639a90dff254244e3aa562158b8d",
      "mcp_contract_sha256": "eb3e39ad4a95ed263415b4932f185d5edfe00a2403267b7c5ed5f718d1ff6da3"
    },
    "contract_checks": {
      "total": 5,
      "passed": 5,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  },
  "tests": [],
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}
