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    "Open-channel specific energy: E = y + v² / (2g); default g=9.80665 m/s²",
    "Invert y = E − v²/(2g) and v = √(2g(E−y)); require E > y",
    "Not a Froude wrap, not a hydraulic jump, not Manning, not Q=Av"
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  "limitations": [
    "Open-channel specific energy: E = y + v² / (2g); default g=9.80665 m/s²",
    "Invert y = E − v²/(2g) and v = √(2g(E−y)); require E > y",
    "Not a Froude wrap, not a hydraulic jump, not Manning, not Q=Av"
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    "missing y, v, or E when required → MISSING_REQUIRED_INPUT",
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    "Fr/L, y1/y2, n, A/Q → MIXED_INPUT_ENCODING",
    "froude, jump, or manning as mode → INVALID_MODE"
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  "sources": [
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      "title": "ISO 80000-4 — Mechanics",
      "section": "Energy, length, speed",
      "supports": "E and y are lengths; v is speed; g is acceleration",
      "kind": "standard"
    },
    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Specific energy",
      "supports": "E = y + v²/(2g) for a rectangular channel with hydrostatic pressure",
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        "v": 2
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        "v": 2,
        "E": 1.2039432425955856,
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        "model": "specific_energy"
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        "E": 1.2039432425955856,
        "y": 1,
        "v": 2,
        "g": 9.80665,
        "model": "specific_energy"
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        "y": 1,
        "v": 1.9999999999999998,
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        "model": "specific_energy"
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      "tol": 1e-12
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        "E": 1.2039432425955856,
        "v": 2
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        "y": 1,
        "v": 2,
        "g": 9.80665,
        "model": "specific_energy"
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    },
    {
      "id": "boundary-se-missing",
      "ok": true,
      "kind": "boundary",
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      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "v is required"
    },
    {
      "id": "boundary-se-Ey",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "velocity",
        "E": 1,
        "y": 1
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "Velocity invert needs E > y"
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    {
      "id": "boundary-se-Fr",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "y": 1,
        "v": 2,
        "Fr": 0.64
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Specific energy does not take Froude Fr or L. That is /calc/physics/froude-number"
    },
    {
      "id": "boundary-se-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "y": 1,
        "v": 2,
        "n": 0.013
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Specific energy does not take Manning n or Chezy C/R/S"
    },
    {
      "id": "boundary-se-A",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "y": 1,
        "v": 2,
        "A": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Specific energy does not take Q=Av A/Q. Use y and v"
    },
    {
      "id": "boundary-se-y1",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "y": 1,
        "v": 2,
        "y1": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Specific energy is not a hydraulic jump. Use y, not y1/y2. That is /calc/physics/hydraulic-jump"
    },
    {
      "id": "boundary-se-L",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "y": 1,
        "v": 2,
        "L": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Specific energy does not take Froude Fr or L. That is /calc/physics/froude-number"
    },
    {
      "id": "boundary-se-froude",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "y": 1,
        "v": 2,
        "mode": "froude"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be energy|depth|velocity. Not Froude, hydraulic jump, Manning, or Q=Av"
    },
    {
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        "v": 0
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