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    "boundary": {
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  "assumptions": [
    "Vena-contracta sudden contraction: h = (1/C_c − 1)² v2² / (2g); default C_c=0.62; K = (1/C_c − 1)² is reported, not an input",
    "Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ K v2² / 2; incompressible; C_c in (0, 1)",
    "Not sudden expansion (v1−v2)², not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av"
  ],
  "limitations": [
    "Vena-contracta sudden contraction: h = (1/C_c − 1)² v2² / (2g); default C_c=0.62; K is reported, not an input",
    "Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ K v2² / 2; incompressible; C_c in (0, 1)",
    "Not sudden expansion (v1−v2)², not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av"
  ],
  "boundary_conditions": [
    "missing v2, h, or C_c when required → MISSING_REQUIRED_INPUT",
    "v2 ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "C_c ≥ 1 → VALUE_OUT_OF_RANGE",
    "v1, K, f/Re, Q, C_d → MIXED_INPUT_ENCODING",
    "expansion, 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 contraction / vena contracta",
      "supports": "Loss from vena contracta to A2 is (v_c−v2)²/(2g) with v_c=v2/C_c; typical sharp-edged C_c≈0.62",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:be3251cbdbad0ee793c810ba3b46f0a5481055b160e746c811ba2bd0cd0bbce3",
  "tests": [
    {
      "id": "golden-sc-h",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "v2": 1
      },
      "expect": {
        "h": 0.019152838339491794,
        "v2": 1,
        "C_c": 0.62,
        "K": 0.37565036420395437,
        "v_c": 1.6129032258064517,
        "dP": 187.8251821019772,
        "mode": "head",
        "model": "vena_contracta"
      },
      "expectWarning": null,
      "actual": {
        "mode": "head",
        "h": 0.019152838339491794,
        "v2": 1,
        "C_c": 0.62,
        "K": 0.37565036420395437,
        "v_c": 1.6129032258064517,
        "g": 9.80665,
        "rho": 1000,
        "dP": 187.8251821019772,
        "model": "vena_contracta"
      },
      "tol": 1e-12
    },
    {
      "id": "golden-sc-dP",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "pressure",
        "v2": 1,
        "C_c": 0.62
      },
      "expect": {
        "dP": 187.8251821019772,
        "model": "vena_contracta"
      },
      "expectWarning": null,
      "actual": {
        "mode": "pressure",
        "h": 0.019152838339491794,
        "v2": 1,
        "C_c": 0.62,
        "K": 0.37565036420395437,
        "v_c": 1.6129032258064517,
        "g": 9.80665,
        "rho": 1000,
        "dP": 187.8251821019772,
        "model": "vena_contracta"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-sc-v2",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "velocity",
        "C_c": 0.62,
        "h": 0.019152838339491794
      },
      "expect": {
        "v2": 1,
        "model": "vena_contracta"
      },
      "expectWarning": null,
      "actual": {
        "mode": "velocity",
        "h": 0.019152838339491794,
        "v2": 1.0000000000000002,
        "C_c": 0.62,
        "K": 0.37565036420395437,
        "v_c": 1.612903225806452,
        "g": 9.80665,
        "rho": 1000,
        "dP": 187.82518210197725,
        "model": "vena_contracta"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-sc-Cc",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "coefficient",
        "v2": 1,
        "h": 0.019152838339491794
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      "expect": {
        "C_c": 0.62,
        "model": "vena_contracta"
      },
      "expectWarning": null,
      "actual": {
        "mode": "coefficient",
        "h": 0.019152838339491794,
        "v2": 1,
        "C_c": 0.62,
        "K": 0.37565036420395437,
        "v_c": 1.6129032258064517,
        "g": 9.80665,
        "rho": 1000,
        "dP": 187.8251821019772,
        "model": "vena_contracta"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-sc-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {},
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "v2 is required"
    },
    {
      "id": "boundary-sc-K",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 1,
        "K": 0.25
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden contraction does not take minor-loss K. That is /calc/physics/minor-loss. K=(1/C_c−1)² is reported"
    },
    {
      "id": "boundary-sc-v1",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 1,
        "v1": 2
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden contraction does not take v1. Borda–Carnot (v1−v2)² is /calc/physics/sudden-expansion"
    },
    {
      "id": "boundary-sc-Cd",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 1,
        "Cd": 0.61
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden contraction does not take orifice C_d or venturi D1/D2. C_c is the vena-contracta coefficient"
    },
    {
      "id": "boundary-sc-Q",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 1,
        "Q": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden contraction does not take Q or A. That is /calc/physics/flow-rate. Give v2 and C_c"
    },
    {
      "id": "boundary-sc-f",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 1,
        "f": 0.02
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Sudden contraction does not take Darcy f, L, D, or Colebrook Re/ε. That is /calc/physics/darcy-weisbach"
    },
    {
      "id": "boundary-sc-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 1,
        "mode": "expansion"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be head|pressure|velocity|coefficient. Not expansion, minor-loss, Darcy, orifice, or Q=Av"
    },
    {
      "id": "boundary-sc-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "v2 must be greater than zero"
    },
    {
      "id": "boundary-sc-Cc1",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v2": 1,
        "C_c": 1
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "C_c must be < 1 (vena contracta is smaller than A2)"
    },
    {
      "id": "property-sc-h",
      "ok": true,
      "kind": "property",
      "detail": "h=(1/C_c−1)² v2²/(2g)",
      "expect": 0.019152838339491794,
      "actual": 0.019152838339491794
    },
    {
      "id": "property-sc-K",
      "ok": true,
      "kind": "property",
      "detail": "K=(1/C_c−1)²",
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      "kind": "property",
      "detail": "vena_contracta",
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