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  "assumptions": [
    "Turbulent circular full-flow pipe, Re ≥ 4000",
    "Incompressible; constant properties",
    "Not laminar 64/Re",
    "Not a Moody-chart lookup",
    "Does not compose Darcy head loss or Reynolds"
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  "limitations": [
    "Turbulent pipes Re ≥ 4000 — not laminar f=64/Re",
    "Not a Moody-chart lookup",
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  "boundary_conditions": [
    "Re < 4000 → VALUE_OUT_OF_RANGE",
    "rel_roughness > 0.05 → VALUE_OUT_OF_RANGE",
    "missing rel_roughness and missing eps_m+D_m → MISSING_REQUIRED_INPUT",
    "rel_roughness together with eps_m+D_m → MIXED_INPUT_ENCODING"
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  "sources": [
    {
      "title": "Colebrook, C.F. (1939). Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws",
      "section": "Journal of the Institution of Civil Engineers, 11, 133–156",
      "supports": "1/√f = −2 log10(ε/D/3.7 + 2.51/(Re √f))",
      "kind": "standard"
    },
    {
      "title": "White, F.M. Fluid Mechanics — pipe flow friction",
      "section": "Colebrook–White equation",
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  "fingerprint": "sha256:d9eae29ee96f8f982c9d408d79a6592f0f95df4fb4080138a201f8026c96821a",
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        "Re": 100000,
        "rel_roughness": 0.0002,
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