{
  "version": 1,
  "topic": "DH06",
  "title": "Darcy versus Fanning friction factors in drilling calculations",
  "createdAt": "2026-10-24",
  "case": {
    "title": "A matched factor convention",
    "premise": "Liquid density 1,000 kg/m³, L = 100 m, D = 0.1 m; Darcy fD = 0.02 and Fanning fF = 0.005.",
    "formula": "ΔpD = fD(L/D)ρv²/2; ΔpF = 4fF(L/D)ρv²/2",
    "variables": "The deliberately wrong calculation inserts fF into the Darcy expression without the factor four.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Velocity (m/s) = 2",
        "explanation": "Liquid density 1,000 kg/m³, L = 100 m, D = 0.1 m; Darcy fD = 0.02 and Fanning fF = 0.005."
      },
      {
        "label": "Select the relation",
        "calculation": "ΔpD = fD(L/D)ρv²/2; ΔpF = 4fF(L/D)ρv²/2",
        "explanation": "The deliberately wrong calculation inserts fF into the Darcy expression without the factor four."
      },
      {
        "label": "Substitute the values",
        "calculation": "0.02 × (100/0.1) × 1,000 × 2²/2 = 40,000 Pa = 40 kPa; 4 × 0.005 gives the same result",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Matched Darcy loss (kPa) = 40; Matched Fanning loss (kPa) = 40; Wrong convention loss (kPa) = 10",
        "explanation": "The two matched conventions agree; the mismatched one underpredicts by four."
      }
    ],
    "result": "Matched Darcy loss (kPa) = 40; Matched Fanning loss (kPa) = 40; Wrong convention loss (kPa) = 10",
    "interpretation": "The two matched conventions agree; the mismatched one underpredicts by four.",
    "control": "Velocity (m/s)",
    "columns": [
      "Velocity (m/s)",
      "Matched Darcy loss (kPa)",
      "Matched Fanning loss (kPa)",
      "Wrong convention loss (kPa)"
    ],
    "rows": [
      [
        0.5,
        2.5,
        2.5,
        0.625
      ],
      [
        1,
        10,
        10,
        2.5
      ],
      [
        2,
        40,
        40,
        10
      ],
      [
        3,
        90,
        90,
        22.5
      ],
      [
        4,
        160,
        160,
        40
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Velocity (m/s) = 0.5. Matched Darcy loss (kPa): 2.5; Matched Fanning loss (kPa): 2.5; Wrong convention loss (kPa): 0.625.",
      "Velocity (m/s) = 1. Matched Darcy loss (kPa): 10; Matched Fanning loss (kPa): 10; Wrong convention loss (kPa): 2.5.",
      "Velocity (m/s) = 2. Matched Darcy loss (kPa): 40; Matched Fanning loss (kPa): 40; Wrong convention loss (kPa): 10.",
      "Velocity (m/s) = 3. Matched Darcy loss (kPa): 90; Matched Fanning loss (kPa): 90; Wrong convention loss (kPa): 22.5.",
      "Velocity (m/s) = 4. Matched Darcy loss (kPa): 160; Matched Fanning loss (kPa): 160; Wrong convention loss (kPa): 40."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Matched Darcy loss (kPa) without rounding intermediate values.",
        "answer": "0.02 × (100/0.1) × 1,000 × 2²/2 = 40,000 Pa = 40 kPa; 4 × 0.005 gives the same result. Matched Darcy loss (kPa) = 40. The two matched conventions agree; the mismatched one underpredicts by four."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Velocity (m/s) changes from 0.5 to 4. Other controls remain as stated in the premise. Matched Darcy loss (kPa) changes from 2.5 to 160."
      },
      {
        "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. The deliberately wrong calculation inserts fF into the Darcy expression without the factor four. The two matched conventions agree; the mismatched one underpredicts by four."
      }
    ]
  },
  "recorded": null
}