{
  "version": 1,
  "topic": "WC09",
  "title": "Hydrostatic pressure versus bottomhole pressure",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Static bottom pressure with a top boundary",
    "premise": "Uniform 10 ppg fluid over 8,000 ft TVD. The top gauge pressure changes; the 4,160 psi fluid head stays fixed.",
    "formula": "Pbottom = Ptop + 0.052 × 10 × 8,000",
    "variables": "All state pressures use the same gauge reference. Flow friction and acceleration are excluded.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Top pressure (psig) = 200",
        "explanation": "Uniform 10 ppg fluid over 8,000 ft TVD. The top gauge pressure changes; the 4,160 psi fluid head stays fixed."
      },
      {
        "label": "Select the relation",
        "calculation": "Pbottom = Ptop + 0.052 × 10 × 8,000",
        "explanation": "All state pressures use the same gauge reference. Flow friction and acceleration are excluded."
      },
      {
        "label": "Substitute the values",
        "calculation": "200 + 0.052 × 10 × 8,000 = 4,360 psig",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Bottom pressure (psig) = 4360; Fluid head (psi) = 4160",
        "explanation": "The boundary shifts bottom pressure one for one without changing hydrostatic head."
      }
    ],
    "result": "Bottom pressure (psig) = 4360; Fluid head (psi) = 4160",
    "interpretation": "The boundary shifts bottom pressure one for one without changing hydrostatic head.",
    "control": "Top pressure (psig)",
    "columns": [
      "Top pressure (psig)",
      "Bottom pressure (psig)",
      "Fluid head (psi)"
    ],
    "rows": [
      [
        0,
        4160,
        4160
      ],
      [
        100,
        4260,
        4160
      ],
      [
        200,
        4360,
        4160
      ],
      [
        450,
        4610,
        4160
      ],
      [
        800,
        4960,
        4160
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Top pressure (psig) = 0. Bottom pressure (psig): 4160; Fluid head (psi): 4160.",
      "Top pressure (psig) = 100. Bottom pressure (psig): 4260; Fluid head (psi): 4160.",
      "Top pressure (psig) = 200. Bottom pressure (psig): 4360; Fluid head (psi): 4160.",
      "Top pressure (psig) = 450. Bottom pressure (psig): 4610; Fluid head (psi): 4160.",
      "Top pressure (psig) = 800. Bottom pressure (psig): 4960; Fluid head (psi): 4160."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Bottom pressure (psig) without rounding intermediate values.",
        "answer": "200 + 0.052 × 10 × 8,000 = 4,360 psig. Bottom pressure (psig) = 4360. The boundary shifts bottom pressure one for one without changing hydrostatic head."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Top pressure (psig) changes from 0 to 800. Other controls remain as stated in the premise. Bottom pressure (psig) changes from 4160 to 4960."
      },
      {
        "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 state pressures use the same gauge reference. Flow friction and acceleration are excluded. The boundary shifts bottom pressure one for one without changing hydrostatic head."
      }
    ]
  },
  "recorded": null
}