{
  "capability_id": "physics.fluid.pitot",
  "tool_id": "pitot-tube",
  "engine": "pitot-tube",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-17T08:49:50.938Z",
  "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/pitot-tube",
  "api": "https://www.calculatorx.com/api/v1/calc/pitot-tube",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.pitot.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.pitot.output.json",
  "assumptions": [
    "Incompressible pitot-static; v = C √(2 Δp / ρ); default C=1",
    "Δp is P0 − P_static at the probe",
    "Not compressible, not a venturi, not an orifice, not Q=Av, not two-station Bernoulli"
  ],
  "limitations": [
    "Incompressible pitot-static: v = C √(2 Δp / ρ); default C=1",
    "Δp is dynamic pressure P0 − P_static; C is a probe coefficient, not orifice C_d",
    "Not a venturi, not an orifice, not Q=Av, not two-station Bernoulli"
  ],
  "boundary_conditions": [
    "missing Δp, ρ, or v when required → MISSING_REQUIRED_INPUT",
    "Δp, ρ, v, or C ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "D1/D2, C_d, A, Q, P1/v1/h1, n, K, Kv → MIXED_INPUT_ENCODING",
    "bernoulli, venturi, or orifice as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 3966 — Measurement of fluid flow in closed conduits — Velocity area method using Pitot static tubes",
      "section": "Pitot-static probes",
      "supports": "Local velocity from dynamic pressure; C is a probe coefficient near 1",
      "kind": "standard"
    },
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Pressure and velocity",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "Dynamic pressure has the dimension of pressure; v has dimension length/time",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:df9f55006c57c30c05fbc60b55e0df94a7e08fea05cf66b60368c1408fc9b7c5",
  "tests": [
    {
      "id": "golden-pt-v",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "dP": 5000,
        "rho": 1000
      },
      "expect": {
        "v": 3.1622776601683795,
        "C": 1,
        "dP": 5000,
        "rho": 1000,
        "mode": "velocity",
        "model": "pitot"
      },
      "expectWarning": null,
      "actual": {
        "mode": "velocity",
        "v": 3.1622776601683795,
        "dP": 5000,
        "rho": 1000,
        "C": 1,
        "model": "pitot"
      },
      "tol": 1e-12
    },
    {
      "id": "golden-pt-c",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "dP": 5000,
        "rho": 1000,
        "C": 0.98
      },
      "expect": {
        "v": 3.0990321069650117,
        "C": 0.98,
        "model": "pitot"
      },
      "expectWarning": null,
      "actual": {
        "mode": "velocity",
        "v": 3.0990321069650117,
        "dP": 5000,
        "rho": 1000,
        "C": 0.98,
        "model": "pitot"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pt-dp",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "pressure",
        "v": 3.1622776601683795,
        "rho": 1000
      },
      "expect": {
        "dP": 5000,
        "model": "pitot"
      },
      "expectWarning": null,
      "actual": {
        "mode": "pressure",
        "v": 3.1622776601683795,
        "dP": 5000.000000000001,
        "rho": 1000,
        "C": 1,
        "model": "pitot"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pt-C",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "C",
        "v": 3.1622776601683795,
        "dP": 5000,
        "rho": 1000
      },
      "expect": {
        "C": 1,
        "model": "pitot"
      },
      "expectWarning": null,
      "actual": {
        "mode": "C",
        "v": 3.1622776601683795,
        "dP": 5000,
        "rho": 1000,
        "C": 1,
        "model": "pitot"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pt-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "rho": 1000
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "dP is required"
    },
    {
      "id": "boundary-pt-dp0",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 0,
        "rho": 1000
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "dP must be greater than zero"
    },
    {
      "id": "boundary-pt-d1",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 5000,
        "rho": 1000,
        "D1": 0.1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pitot does not take venturi D1/D2 or orifice d. That is /calc/physics/venturi or /calc/physics/orifice-discharge"
    },
    {
      "id": "boundary-pt-A",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 5000,
        "rho": 1000,
        "A": 0.002
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pitot does not take Q=Av A/Q. That is /calc/physics/flow-rate"
    },
    {
      "id": "boundary-pt-P1",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 5000,
        "rho": 1000,
        "P1": 101325
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pitot is not two-station Bernoulli. That is /calc/physics/bernoulli. Give Δp = P0 − P_static"
    },
    {
      "id": "boundary-pt-bernoulli",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 5000,
        "rho": 1000,
        "mode": "bernoulli"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be velocity|pressure|C. Not Bernoulli, venturi, orifice, or Q=Av"
    },
    {
      "id": "boundary-pt-Cd",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 5000,
        "rho": 1000,
        "Cd": 0.61
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pitot C is not orifice or venturi C_d. Give pitot C or omit for 1"
    },
    {
      "id": "boundary-pt-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 5000,
        "rho": 1000,
        "n": 0.013
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pitot does not take tank H, Manning n, Chezy R/S, Darcy f, minor-loss K, or valve Kv/Cv"
    },
    {
      "id": "property-pt-v",
      "ok": true,
      "kind": "property",
      "detail": "v=√(2Δp/ρ)",
      "expect": 3.1622776601683795,
      "actual": 3.1622776601683795
    },
    {
      "id": "property-pt-C-default",
      "ok": true,
      "kind": "property",
      "detail": "default C=1",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-pt-roundtrip-dp",
      "ok": true,
      "kind": "property",
      "detail": "Δp invert",
      "expect": 5000,
      "actual": 5000.000000000001
    },
    {
      "id": "property-pt-roundtrip-C",
      "ok": true,
      "kind": "property",
      "detail": "C invert",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-pt-model",
      "ok": true,
      "kind": "property",
      "detail": "pitot",
      "expect": true,
      "actual": "pitot"
    }
  ],
  "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": "2026-09-17T06:50:47.586Z",
  "rendered_at": "2026-09-17T08:49:50.938Z",
  "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": "3d2b0288ca0d60d77024070ce92d740aab36efe992b69c32fa9ac1325e302f69",
      "output_schema_sha256": "4af43f43f88a42898996fac30d314a3e694e36882c3f34037c80a2dcc17f62b9",
      "evidence_sha256": "f31c7acaacccc4c1fbf35864c9839d8fee8980373cb9ef25618eb0159921cbe6",
      "evidence_core_sha256": "f31c7acaacccc4c1fbf35864c9839d8fee8980373cb9ef25618eb0159921cbe6",
      "capability_sha256": "ece61acb924dab7585c1f231d503b4139173aca17201db4ce0155b3758a48bf0",
      "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"
  }
}