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      "sources",
      "tests"
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  "assumptions": [
    "D_h = 4 A / P_w; R = A / P_w = D_h / 4",
    "Full circular pipe: D_h = D; closed rectangular duct: D_h = 2ab/(a+b); annulus: D_h = D_o − D_i",
    "Not Q=Av, not Manning Q, not Reynolds, not Darcy, not a weir or orifice"
  ],
  "limitations": [
    "D_h = 4 A / P_w; R = A / P_w = D_h / 4",
    "Full circular pipe: D_h = D; closed rectangular duct: D_h = 2ab/(a+b); annulus: D_h = D_o − D_i",
    "Not Q=Av, not Manning Q, not Reynolds, not Darcy, not a weir or orifice"
  ],
  "boundary_conditions": [
    "missing A+Pw, R, circular D, rectangular a+b, or annular D_o+D_i → MISSING_REQUIRED_INPUT",
    "A, Pw, R, D, a, b, D_o, or D_i ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "annulus D_i ≥ D_o → VALUE_OUT_OF_RANGE",
    "A+Pw+R, R+Dh, Q, v, n, f, C_d, or NPSH/pump fields → MIXED_INPUT_ENCODING",
    "manning, flow, reynolds, darcy, weir, orifice, pump, or NPSH as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 5167-1 — Measurement of fluid flow by means of pressure differential devices",
      "section": "Hydraulic diameter",
      "url": "https://www.iso.org/standard/17583.html",
      "supports": "D_h = 4A/P for non-circular conduits; annulus D_h = D_o − D_i",
      "kind": "standard"
    },
    {
      "title": "White, F.M. Fluid Mechanics",
      "section": "Noncircular ducts",
      "supports": "Equivalent diameter D_h=4A/P; rectangular duct 2ab/(a+b)",
      "kind": "reference"
    }
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      "ok": true,
      "kind": "golden",
      "inputs": {
        "A": 0.01,
        "Pw": 0.4
      },
      "expect": {
        "Dh": 0.1,
        "R": 0.025,
        "A": 0.01,
        "Pw": 0.4,
        "mode": "general",
        "model": "hydraulic_diameter"
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      "actual": {
        "mode": "general",
        "Dh": 0.09999999999999999,
        "R": 0.024999999999999998,
        "A": 0.01,
        "Pw": 0.4,
        "model": "hydraulic_diameter"
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      "tol": 1e-12
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    {
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      "ok": true,
      "kind": "golden",
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        "D": 0.1
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        "D": 0.1,
        "model": "hydraulic_diameter"
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      "actual": {
        "mode": "circular",
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        "R": 0.025,
        "A": 0.007853981633974483,
        "Pw": 0.3141592653589793,
        "model": "hydraulic_diameter",
        "D": 0.1
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      "tol": 1e-12
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    {
      "id": "boundary-dh-rect",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rectangular",
        "a": 0.2,
        "b": 0.1
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      "expect": {
        "Dh": 0.13333333333333333,
        "a": 0.2,
        "b": 0.1,
        "model": "hydraulic_diameter"
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      "expectWarning": null,
      "actual": {
        "mode": "rectangular",
        "Dh": 0.13333333333333333,
        "R": 0.03333333333333333,
        "A": 0.020000000000000004,
        "Pw": 0.6000000000000001,
        "model": "hydraulic_diameter",
        "a": 0.2,
        "b": 0.1
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      "tol": 1e-12
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    {
      "id": "boundary-dh-annulus",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "annular",
        "D_o": 0.1,
        "D_i": 0.06
      },
      "expect": {
        "Dh": 0.04,
        "model": "hydraulic_diameter"
      },
      "expectWarning": null,
      "actual": {
        "mode": "annular",
        "Dh": 0.04000000000000001,
        "R": 0.010000000000000002,
        "A": 0.005026548245743671,
        "Pw": 0.5026548245743669,
        "model": "hydraulic_diameter",
        "D_o": 0.1,
        "D_i": 0.06
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      "tol": 1e-12
    },
    {
      "id": "boundary-dh-from-r",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "R": 0.025
      },
      "expect": {
        "Dh": 0.1,
        "R": 0.025,
        "model": "hydraulic_diameter"
      },
      "expectWarning": null,
      "actual": {
        "mode": "general",
        "Dh": 0.1,
        "R": 0.025,
        "model": "hydraulic_diameter"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-dh-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "A": 0.01
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "Need A and Pw, or R, or A and Dh, or Pw and Dh"
    },
    {
      "id": "boundary-dh-a0",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "A": 0,
        "Pw": 0.4
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "A must be greater than zero"
    },
    {
      "id": "boundary-dh-mixed",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "A": 0.01,
        "Pw": 0.4,
        "R": 0.025
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Give A+Pw, A+Dh, Pw+Dh, or R — not three encodings"
    },
    {
      "id": "boundary-dh-q",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "A": 0.01,
        "Pw": 0.4,
        "Q": 0.02
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Hydraulic diameter does not take Q. That is Q=Av or Manning"
    },
    {
      "id": "boundary-dh-manning",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "A": 0.01,
        "Pw": 0.4,
        "mode": "manning"
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      "actual": 0.09999999999999999
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      "expect": 0.025,
      "actual": 0.024999999999999998
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      "detail": "D_h=D",
      "expect": 0.1,
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      "ok": true,
      "kind": "property",
      "detail": "2ab/(a+b)",
      "expect": 0.13333333333333333,
      "actual": 0.13333333333333333
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      "ok": true,
      "kind": "property",
      "detail": "D_h=4R",
      "expect": 0.1,
      "actual": 0.1
    }
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