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  "assumptions": [
    "Trapezoid critical depth: Fr=1 with A=(b+z yc) yc and T=b+2 z yc so Q² T = g A³; SI; default g=9.80665; z>0 is run/rise",
    "Critical speed vc = Q/A = √(g A/T) is reported, not an input; Fr=1 is the definition, not a Froude wrap",
    "Not rectangular yc=(q²/g)^{1/3}; not normal-depth yn; not specific energy E; not Manning n; not Q=Av"
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    "Trapezoid critical depth: Fr=1 with A=(b+z yc) yc and T=b+2 z yc so Q² T = g A³; SI; default g=9.80665; z>0 is run/rise",
    "Unknown is yc (depth mode) or Q (discharge invert); vc=√(g A/T) is reported; Fr=1 is the definition, not a Froude wrap",
    "Not rectangular yc=(q²/g)^{1/3}; not normal-depth yn; not specific energy E; not Manning n; not Q=Av"
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    "z=0, q, n/S/yn, E, Fr/L, A/v, y1/M/Sc, B, theta → MIXED_INPUT_ENCODING",
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      "section": "Length, speed, acceleration",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "yc is a length; Q is volume flow; g is acceleration",
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    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Critical flow in a trapezoidal section",
      "supports": "Fr=1 is Q² T = g A³. Rectangular yc=(q²/g)^{1/3} is the z=0 special case on a different page.",
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      "detail": "Q²T=gA³",
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