{
  "capability_id": "physics.fluid.venturi",
  "tool_id": "venturi",
  "engine": "venturi",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-17T06:35:12.147Z",
  "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
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  "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
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  "page": "https://www.calculatorx.com/calc/physics/venturi",
  "api": "https://www.calculatorx.com/api/v1/calc/venturi",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.venturi.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.venturi.output.json",
  "assumptions": [
    "Incompressible venturi tube; SI; default C_d=0.98; C_d in (0, 1]",
    "Q=C_d A2 √(2Δp/(ρ(1−β⁴))), β=D2/D1; Q_ideal uses C_d=1",
    "Optional same-fluid manometer Δh with Δp=ρ g Δh; not tank H",
    "Not an orifice plate, not Q=Av, not Darcy, not minor-loss K, not valve Cv/Kv"
  ],
  "limitations": [
    "Incompressible venturi: Q = C_d A2 √(2Δp/(ρ(1−β⁴))), β=D2/D1; default C_d=0.98",
    "Ideal Bernoulli Q_ideal uses C_d=1; optional same-fluid manometer Δh, Δp=ρ g Δh",
    "Not an orifice plate, not Q=Av, not Darcy, not minor-loss K, not valve Cv/Kv"
  ],
  "boundary_conditions": [
    "missing D1, D2, Δp/Δh, Q, or ρ when required → MISSING_REQUIRED_INPUT",
    "D1, D2, Δp, Δh, Q, ρ, or C_d ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "D2 ≥ D1 or inverted C_d > 1 → VALUE_OUT_OF_RANGE",
    "orifice d or D, tank H, A, v, Cv/Kv, K, f, n, C, Q with flow → MIXED_INPUT_ENCODING",
    "orifice, tank, weir, darcy, or Cv as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 5167-4 — Measurement of fluid flow by means of pressure differential devices — Venturi tubes",
      "section": "Incompressible discharge with velocity-of-approach factor",
      "url": "https://www.iso.org/standard/30192.html",
      "supports": "Q = C E (π/4) D2² √(2Δp/ρ); E = 1/√(1−β⁴); this page takes C as an input with default 0.98",
      "kind": "standard"
    },
    {
      "title": "White, F.M. Fluid Mechanics",
      "section": "Venturi meter from Bernoulli plus continuity",
      "supports": "Ideal Q = A2 √(2Δp/(ρ(1−β⁴))); a discharge coefficient C_d < 1 accounts for losses",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:a8883abb131362b9a281b5c4790a515f8c17b6890ef76f0040c477af31316db2",
  "tests": [
    {
      "id": "golden-vt-q",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "dP": 10000,
        "rho": 1000
      },
      "expect": {
        "Q": 0.008887616884747668,
        "Cd": 0.98,
        "mode": "flow",
        "model": "venturi"
      },
      "expectWarning": null,
      "actual": {
        "mode": "flow",
        "Q": 0.008887616884747668,
        "Q_ideal": 0.00906899682117109,
        "D1": 0.1,
        "D2": 0.05,
        "beta": 0.5,
        "E": 1.0327955589886444,
        "A1": 0.007853981633974483,
        "A2": 0.001963495408493621,
        "v1": 1.1316065276116665,
        "v2": 4.526426110446666,
        "Cd": 0.98,
        "g": 9.80665,
        "dP": 10000,
        "dH": 1.0197162129779282,
        "model": "venturi",
        "rho": 1000
      },
      "tol": 1e-12
    },
    {
      "id": "golden-vt-dh",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "dH": 1.0197162129779282,
        "rho": 1000
      },
      "expect": {
        "Q": 0.008887616884747668,
        "dP": 10000,
        "model": "venturi"
      },
      "expectWarning": null,
      "actual": {
        "mode": "flow",
        "Q": 0.008887616884747668,
        "Q_ideal": 0.00906899682117109,
        "D1": 0.1,
        "D2": 0.05,
        "beta": 0.5,
        "E": 1.0327955589886444,
        "A1": 0.007853981633974483,
        "A2": 0.001963495408493621,
        "v1": 1.1316065276116665,
        "v2": 4.526426110446666,
        "Cd": 0.98,
        "g": 9.80665,
        "dP": 10000,
        "dH": 1.0197162129779282,
        "model": "venturi",
        "rho": 1000
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-vt-dp",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "pressure",
        "D1": 0.1,
        "D2": 0.05,
        "Q": 0.008887616884747668,
        "rho": 1000
      },
      "expect": {
        "dP": 10000,
        "model": "venturi"
      },
      "expectWarning": null,
      "actual": {
        "mode": "pressure",
        "Q": 0.008887616884747668,
        "Q_ideal": 0.00906899682117109,
        "D1": 0.1,
        "D2": 0.05,
        "beta": 0.5,
        "E": 1.0327955589886444,
        "A1": 0.007853981633974483,
        "A2": 0.001963495408493621,
        "v1": 1.1316065276116665,
        "v2": 4.526426110446666,
        "Cd": 0.98,
        "g": 9.80665,
        "dP": 10000.000000000002,
        "dH": 1.0197162129779285,
        "model": "venturi",
        "rho": 1000
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-vt-d2",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "throat",
        "D1": 0.1,
        "Q": 0.008887616884747668,
        "dP": 10000,
        "rho": 1000
      },
      "expect": {
        "D2": 0.05,
        "model": "venturi"
      },
      "expectWarning": null,
      "actual": {
        "mode": "throat",
        "Q": 0.008887616884747668,
        "Q_ideal": 0.00906899682117109,
        "D1": 0.1,
        "D2": 0.05,
        "beta": 0.5,
        "E": 1.0327955589886444,
        "A1": 0.007853981633974483,
        "A2": 0.001963495408493621,
        "v1": 1.1316065276116665,
        "v2": 4.526426110446666,
        "Cd": 0.98,
        "g": 9.80665,
        "dP": 10000,
        "dH": 1.0197162129779282,
        "model": "venturi",
        "rho": 1000
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-vt-cd",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "Cd",
        "D1": 0.1,
        "D2": 0.05,
        "Q": 0.008887616884747668,
        "dP": 10000,
        "rho": 1000
      },
      "expect": {
        "Cd": 0.98,
        "model": "venturi"
      },
      "expectWarning": null,
      "actual": {
        "mode": "Cd",
        "Q": 0.008887616884747668,
        "Q_ideal": 0.009068996821171089,
        "D1": 0.1,
        "D2": 0.05,
        "beta": 0.5,
        "E": 1.0327955589886444,
        "A1": 0.007853981633974483,
        "A2": 0.001963495408493621,
        "v1": 1.1316065276116665,
        "v2": 4.526426110446666,
        "Cd": 0.9800000000000002,
        "g": 9.80665,
        "dP": 10000,
        "dH": 1.0197162129779282,
        "model": "venturi",
        "rho": 1000
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-vt-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "rho": 1000
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "Need Δp (with ρ) or same-fluid Δh"
    },
    {
      "id": "boundary-vt-d2ge",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D1": 0.1,
        "D2": 0.1,
        "dP": 10000,
        "rho": 1000
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "throat D2 must be smaller than inlet D1"
    },
    {
      "id": "boundary-vt-orifice-d",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "dP": 10000,
        "rho": 1000,
        "d": 0.05
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Venturi takes throat D2, not orifice d. That is /calc/physics/orifice-discharge"
    },
    {
      "id": "boundary-vt-cv",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "dP": 10000,
        "rho": 1000,
        "Cv": 10
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Venturi is not valve Cv/Kv"
    },
    {
      "id": "boundary-vt-qav",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "dP": 10000,
        "rho": 1000,
        "A": 0.002
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Venturi does not take Q=Av A or v. Give D1 and D2"
    },
    {
      "id": "boundary-vt-orifice-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "dP": 10000,
        "rho": 1000,
        "mode": "orifice"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be flow|pressure|throat|Cd. Not orifice, Q=Av, Darcy, or Cv/Kv"
    },
    {
      "id": "boundary-vt-tank-h",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D1": 0.1,
        "D2": 0.05,
        "dP": 10000,
        "rho": 1000,
        "H": 2
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Venturi does not take tank/weir H. Use dP or same-fluid dH"
    },
    {
      "id": "property-vt-q",
      "ok": true,
      "kind": "property",
      "detail": "Cd E A2 √(2Δp/ρ)",
      "expect": 0.008887616884747668,
      "actual": 0.008887616884747668
    },
    {
      "id": "property-vt-ideal",
      "ok": true,
      "kind": "property",
      "detail": "Q=Cd Q_ideal",
      "expect": 0.008887616884747668,
      "actual": 0.008887616884747668
    },
    {
      "id": "property-vt-roundtrip-dp",
      "ok": true,
      "kind": "property",
      "detail": "Δp invert",
      "expect": 10000,
      "actual": 10000.000000000002
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    {
      "id": "property-vt-dh",
      "ok": true,
      "kind": "property",
      "detail": "Δh encoding",
      "expect": 0.008887616884747668,
      "actual": 0.008887616884747668
    },
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      "id": "property-vt-model",
      "ok": true,
      "kind": "property",
      "detail": "venturi",
      "expect": true,
      "actual": "venturi"
    }
  ],
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      "passed": 17,
      "total": 17,
      "golden": 2,
      "boundary": 10,
      "property": 5
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