{
  "version": 1,
  "topic": "PR06",
  "title": "Separator gas capacity versus liquid retention time",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Nominal effective-volume retention",
    "premise": "Effective liquid working volume 10 m³. Local liquid throughput varies; total vessel shell volume is not used.",
    "formula": "tret = Veffective/Qlocal",
    "variables": "Q in m³/min produces time in minutes. This inventory time differs from a viscosity/density-based required separation-time correlation.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Liquid throughput (m³/min) = 2",
        "explanation": "Effective liquid working volume 10 m³. Local liquid throughput varies; total vessel shell volume is not used."
      },
      {
        "label": "Select the relation",
        "calculation": "tret = Veffective/Qlocal",
        "explanation": "Q in m³/min produces time in minutes. This inventory time differs from a viscosity/density-based required separation-time correlation."
      },
      {
        "label": "Substitute the values",
        "calculation": "10 m³/(2 m³/min) = 5 min",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Nominal retention (min) = 5",
        "explanation": "V/Q is nominal retention; gas capacity and droplet-separation performance need separate checks."
      }
    ],
    "result": "Nominal retention (min) = 5",
    "interpretation": "V/Q is nominal retention; gas capacity and droplet-separation performance need separate checks.",
    "control": "Liquid throughput (m³/min)",
    "columns": [
      "Liquid throughput (m³/min)",
      "Nominal retention (min)"
    ],
    "rows": [
      [
        0.5,
        20
      ],
      [
        1,
        10
      ],
      [
        2,
        5
      ],
      [
        4,
        2.5
      ],
      [
        5,
        2
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Liquid throughput (m³/min) = 0.5. Nominal retention (min): 20.",
      "Liquid throughput (m³/min) = 1. Nominal retention (min): 10.",
      "Liquid throughput (m³/min) = 2. Nominal retention (min): 5.",
      "Liquid throughput (m³/min) = 4. Nominal retention (min): 2.5.",
      "Liquid throughput (m³/min) = 5. Nominal retention (min): 2."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Nominal retention (min) without rounding intermediate values.",
        "answer": "10 m³/(2 m³/min) = 5 min. Nominal retention (min) = 5. V/Q is nominal retention; gas capacity and droplet-separation performance need separate checks."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Liquid throughput (m³/min) changes from 0.5 to 5. Other controls remain as stated in the premise. Nominal retention (min) changes from 20 to 2."
      },
      {
        "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. Q in m³/min produces time in minutes. This inventory time differs from a viscosity/density-based required separation-time correlation. V/Q is nominal retention; gas capacity and droplet-separation performance need separate checks."
      }
    ]
  },
  "recorded": null
}