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    "Equal-area sharp wye: h = K v_c² / (2g); K referenced to common-channel speed; α ∈ (0, 90°); K is reported, not an input",
    "Branch K=1+q²−2q cos α. Dividing run K=0.4(1−q)². Combining run K=1−q²−2q(1−q)cos α. q=Q_path/Q_c in [0,1]; default g=9.80665 m/s²; default ρ=1000 kg/m³",
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    "Equal-area sharp wye: h = K v_c² / (2g); K referenced to common-channel speed; α ∈ (0, 90°); K is reported, not an input",
    "Branch K=1+q²−2q cos α. Dividing run K=0.4(1−q)². Combining run K=1−q²−2q(1−q)cos α. q=Q_path/Q_c in [0,1]; default g=9.80665; default ρ=1000 for Δp",
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    "q_ratio > 1, α ∉ (0, 90), or K=0 on velocity invert → VALUE_OUT_OF_RANGE",
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      "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",
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      "title": "Idelchik — Handbook of Hydraulic Resistance",
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