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    "boundary": {
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      "sources",
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  "assumptions": [
    "Borda–Carnot sudden expansion: h = (v1 − v2)² / (2g); K = (1 − v2/v1)² is reported, not an input",
    "Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ (v1−v2)² / 2; incompressible; A2 > A1",
    "Not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av, not sudden contraction"
  ],
  "limitations": [
    "Borda–Carnot sudden expansion: h = (v1 − v2)² / (2g); K = (1 − v2/v1)² is reported, not an input",
    "Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ (v1−v2)² / 2; incompressible; A2 > A1",
    "Not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av, not sudden contraction"
  ],
  "boundary_conditions": [
    "missing v1, v2, h, or A1 when required → MISSING_REQUIRED_INPUT",
    "v1 ≤ 0, h ≤ 0, or A1 ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "v2 ≥ v1 → VALUE_OUT_OF_RANGE",
    "K, f/Re, Q, C_d → MIXED_INPUT_ENCODING",
    "minor, darcy, or orifice as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Length, speed, pressure",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "h is a head; v is a speed; Δp is a pressure",
      "kind": "standard"
    },
    {
      "title": "Borda–Carnot equation",
      "section": "Sudden enlargement",
      "supports": "h=(v1−v2)²/(2g) for incompressible sudden expansion; K=(1−A1/A2)²",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:ed9626814e473ec68773b087522fb135943bb1420a37dfc0299249f5584764ae",
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    {
      "id": "golden-se-h",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "v1": 2,
        "v2": 1
      },
      "expect": {
        "h": 0.050985810648896415,
        "v1": 2,
        "v2": 1,
        "K": 0.25,
        "dP": 500,
        "mode": "head",
        "model": "borda_carnot"
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      "expectWarning": null,
      "actual": {
        "mode": "head",
        "h": 0.050985810648896415,
        "v1": 2,
        "v2": 1,
        "K": 0.25,
        "g": 9.80665,
        "rho": 1000,
        "dP": 500,
        "model": "borda_carnot"
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      "tol": 1e-12
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    {
      "id": "golden-se-dP",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "pressure",
        "v1": 2,
        "v2": 1
      },
      "expect": {
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        "model": "borda_carnot"
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      "expectWarning": null,
      "actual": {
        "mode": "pressure",
        "h": 0.050985810648896415,
        "v1": 2,
        "v2": 1,
        "K": 0.25,
        "g": 9.80665,
        "rho": 1000,
        "dP": 500,
        "model": "borda_carnot"
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      "tol": 1e-12
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    {
      "id": "boundary-se-v2",
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        "h": 0.050985810648896415
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        "model": "borda_carnot"
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      "actual": {
        "mode": "velocity",
        "h": 0.050985810648896415,
        "v1": 2,
        "v2": 1,
        "K": 0.25,
        "g": 9.80665,
        "rho": 1000,
        "dP": 500,
        "model": "borda_carnot"
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      "tol": 1e-12
    },
    {
      "id": "boundary-se-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 2
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "v2 is required"
    },
    {
      "id": "boundary-se-K",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 2,
        "v2": 1,
        "K": 0.25
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden expansion does not take minor-loss K. That is /calc/physics/minor-loss. K=(1−v2/v1)² is reported"
    },
    {
      "id": "boundary-se-f",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 2,
        "v2": 1,
        "f": 0.02
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden expansion does not take Darcy f, L, D, or Colebrook Re/ε. That is /calc/physics/darcy-weisbach"
    },
    {
      "id": "boundary-se-Q",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 2,
        "v2": 1,
        "Q": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden expansion does not take Q or A. That is /calc/physics/flow-rate. Give v1 and v2, or A1 on the A2 tab"
    },
    {
      "id": "boundary-se-Cd",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 2,
        "v2": 1,
        "Cd": 0.61
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden expansion does not take orifice C_d or venturi D1/D2"
    },
    {
      "id": "boundary-se-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 2,
        "v2": 1,
        "mode": "minor"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be head|pressure|velocity|area. Not minor-loss, Darcy, orifice, or Q=Av"
    },
    {
      "id": "boundary-se-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 0,
        "v2": 1
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "v1 must be greater than zero"
    },
    {
      "id": "boundary-se-contract",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 1,
        "v2": 2
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "Sudden expansion needs v1 > v2. Contraction is not this page"
    },
    {
      "id": "boundary-se-A2",
      "ok": true,
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      "inputs": {
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        "A1": 1,
        "v1": 2,
        "h": 0.050985810648896415
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      "expect": {
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        "model": "borda_carnot"
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      "expectWarning": null,
      "actual": {
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        "K": 0.25,
        "g": 9.80665,
        "rho": 1000,
        "dP": 500,
        "model": "borda_carnot",
        "A1": 1,
        "A2": 2
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      "tol": 1e-12
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      "actual": 0.050985810648896415
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      "kind": "property",
      "detail": "v2 invert",
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      "kind": "property",
      "detail": "Δp=500",
      "expect": 500,
      "actual": 500
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      "ok": true,
      "kind": "property",
      "detail": "borda_carnot",
      "expect": true,
      "actual": "borda_carnot"
    }
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