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    "Rectangular uniform flow: Q=(1/n) A R^{2/3} S^{1/2}; A=b yn; R=b yn/(b+2 yn); SI k=1; yn is unknown in depth mode",
    "yn/b∈[0.01, 10]; n∈[0.008, 0.15]; S∈[1e-6, 0.1]; geometry is b, not A and R",
    "Not Manning Q with given A,R; not critical depth yc=(q²/g)^{1/3}; not specific energy E; not Chezy C; not Q=Av"
  ],
  "limitations": [
    "Rectangular uniform-flow normal depth: invert SI Manning Q=(1/n) A R^{2/3} S^{1/2} with A=b yn, R=b yn/(b+2 yn); yn is unknown; n, S, b given",
    "yn/b∈[0.01, 10]; n∈[0.008, 0.15]; S∈[1e-6, 0.1]; SI k=1; geometry is rectangular width b, not A and R",
    "Not Manning Q with given A,R; not critical depth yc=(q²/g)^{1/3}; not specific energy E; not Chezy C; not Q=Av"
  ],
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    "A/R, yc/q, E, Chezy C, v, B, z, y1, H → MIXED_INPUT_ENCODING",
    "unknown mode → INVALID_MODE"
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      "title": "ISO 80000-4 — Mechanics",
      "section": "Volume flow rate and hydraulic radius",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "Q is volume flow; hydraulic radius R = A/P",
      "kind": "standard"
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    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Normal depth in uniform flow",
      "supports": "Uniform-flow yn from SI Manning with rectangular A=b yn and R=A/(b+2 yn). Not Manning with given A,R as a product page, not yc, not E, not Chezy C",
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