{
  "version": 1,
  "topic": "PR11",
  "title": "Why the same standard gas rate has different pipe velocity",
  "createdAt": "2026-10-24",
  "case": {
    "title": "One standard gas rate, different actual speeds",
    "premise": "Standard rate 1 m³/s at 101,325 Pa, 288.15 K and Zs = 1. Local T = 320 K, Z = 0.9, pipe ID = 0.1 m.",
    "formula": "Qactual = Qstd(ZT/P)/(ZsTs/Ps); v = Qactual/(πD²/4)",
    "variables": "All pressures are absolute. Standard cubic metres per second are used here to make the SI state ratio explicit.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Local absolute pressure (MPa) = 2",
        "explanation": "Standard rate 1 m³/s at 101,325 Pa, 288.15 K and Zs = 1. Local T = 320 K, Z = 0.9, pipe ID = 0.1 m."
      },
      {
        "label": "Select the relation",
        "calculation": "Qactual = Qstd(ZT/P)/(ZsTs/Ps); v = Qactual/(πD²/4)",
        "explanation": "All pressures are absolute. Standard cubic metres per second are used here to make the SI state ratio explicit."
      },
      {
        "label": "Substitute the values",
        "calculation": "At 2 MPa: Q = 1 × 0.9 × 320 × 101,325/(2,000,000 × 288.15); divide by π × 0.1²/4 for speed",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Actual gas rate (m³/s) = 0.050636127; Gas speed (m/s) = 6.44719193",
        "explanation": "Constant standard rate does not mean constant local volumetric rate or velocity."
      }
    ],
    "result": "Actual gas rate (m³/s) = 0.050636127; Gas speed (m/s) = 6.44719193",
    "interpretation": "Constant standard rate does not mean constant local volumetric rate or velocity.",
    "control": "Local absolute pressure (MPa)",
    "columns": [
      "Local absolute pressure (MPa)",
      "Actual gas rate (m³/s)",
      "Gas speed (m/s)"
    ],
    "rows": [
      [
        0.5,
        0.2025445080687142,
        25.788767724201715
      ],
      [
        1,
        0.1012722540343571,
        12.894383862100858
      ],
      [
        2,
        0.05063612701717855,
        6.447191931050429
      ],
      [
        5,
        0.02025445080687142,
        2.5788767724201715
      ],
      [
        10,
        0.01012722540343571,
        1.2894383862100858
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Local absolute pressure (MPa) = 0.5. Actual gas rate (m³/s): 0.202544508; Gas speed (m/s): 25.7887677.",
      "Local absolute pressure (MPa) = 1. Actual gas rate (m³/s): 0.101272254; Gas speed (m/s): 12.8943839.",
      "Local absolute pressure (MPa) = 2. Actual gas rate (m³/s): 0.050636127; Gas speed (m/s): 6.44719193.",
      "Local absolute pressure (MPa) = 5. Actual gas rate (m³/s): 0.0202544508; Gas speed (m/s): 2.57887677.",
      "Local absolute pressure (MPa) = 10. Actual gas rate (m³/s): 0.0101272254; Gas speed (m/s): 1.28943839."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Actual gas rate (m³/s) without rounding intermediate values.",
        "answer": "At 2 MPa: Q = 1 × 0.9 × 320 × 101,325/(2,000,000 × 288.15); divide by π × 0.1²/4 for speed. Actual gas rate (m³/s) = 0.050636127. Constant standard rate does not mean constant local volumetric rate or velocity."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Local absolute pressure (MPa) changes from 0.5 to 10. Other controls remain as stated in the premise. Actual gas rate (m³/s) changes from 0.202544508 to 0.0101272254."
      },
      {
        "question": "What would be needed to apply this example to a different physical system?",
        "answer": "Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. All pressures are absolute. Standard cubic metres per second are used here to make the SI state ratio explicit. Constant standard rate does not mean constant local volumetric rate or velocity."
      }
    ]
  },
  "recorded": null
}