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  "assumptions": [
    "Equal-area sharp 90° T: h = K v_c² / (2g); K referenced to common-channel speed; K is reported, not an input",
    "Dividing: branch K=1+q², run K=0.4(1−q)². Combining: branch K=1+q², run K=1.55q−q². q=Q_path/Q_c in [0,1]; default g=9.80665 m/s²; default ρ=1000 kg/m³",
    "Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not a non-90° wye, not Q=Av"
  ],
  "limitations": [
    "Equal-area sharp 90° T: h = K v_c² / (2g); K referenced to common-channel speed; K is reported, not an input",
    "Dividing: branch K=1+q², run K=0.4(1−q)². Combining: branch K=1+q², run K=1.55q−q². q=Q_path/Q_c in [0,1]; default g=9.80665; default ρ=1000 for Δp",
    "Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not a non-90° wye, not Q=Av"
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  "boundary_conditions": [
    "missing v_m_s, h, or q_ratio when required → MISSING_REQUIRED_INPUT",
    "v_m_s ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "q_ratio > 1 or K=0 on velocity invert → VALUE_OUT_OF_RANGE",
    "K, rd, n_miters, θ, α, f, Q, A, v1/v2, ri_d → MIXED_INPUT_ENCODING",
    "flush, circular, or unknown kind/path/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": "Idelchik — Handbook of Hydraulic Resistance",
      "section": "Diagrams 7-18 / 7-20 No.1 (dividing) and 7-1 / 7-4 (combining), equal-area 90° T",
      "supports": "Branch K=1+q²; dividing run K=0.4(1−q)²; combining run K=1.55q−q²; K referenced to v_c. Not catalog K, not a bend, not entrance/exit",
      "kind": "reference"
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  "methods": [],
  "fingerprint": "sha256:de70d79fa6d7b1fb4b32733d581c69ae1ea12d33e9891a661638ae432e476eec",
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      "ok": true,
      "kind": "property",
      "detail": "h=K v_c²/(2g) dividing branch",
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      "ok": true,
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      "detail": "K=1+q²",
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      "detail": "dividing run K=0.4(1−q)²",
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      "id": "property-tee-comb",
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      "detail": "combining run K=1.55q−q²",
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      "golden": 0,
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      "property": 6
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