{
  "version": 1,
  "topic": "FA05",
  "title": "Water hammer versus a steady pressure loss calculation",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Ideal rapid velocity-change pressure increment",
    "premise": "ρ = 1,000 kg/m³, wave speed a = 1,000 m/s. Pipe L = 1,000 m gives round-trip wave time 2 s.",
    "formula": "Δp = ρaΔv",
    "variables": "This is the analytical Joukowsky estimate, not a full closure-time or reflection history. Δv is a positive velocity-reduction magnitude.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Velocity reduction (m/s) = 0.5",
        "explanation": "ρ = 1,000 kg/m³, wave speed a = 1,000 m/s. Pipe L = 1,000 m gives round-trip wave time 2 s."
      },
      {
        "label": "Select the relation",
        "calculation": "Δp = ρaΔv",
        "explanation": "This is the analytical Joukowsky estimate, not a full closure-time or reflection history. Δv is a positive velocity-reduction magnitude."
      },
      {
        "label": "Substitute the values",
        "calculation": "1,000 × 1,000 × 0.5 = 500,000 Pa = 0.5 MPa",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Ideal pressure increment (MPa) = 0.5",
        "explanation": "A transient workflow is required for time evolution, reflections and supported boundary behavior."
      }
    ],
    "result": "Ideal pressure increment (MPa) = 0.5",
    "interpretation": "A transient workflow is required for time evolution, reflections and supported boundary behavior.",
    "control": "Velocity reduction (m/s)",
    "columns": [
      "Velocity reduction (m/s)",
      "Ideal pressure increment (MPa)"
    ],
    "rows": [
      [
        0.1,
        0.1
      ],
      [
        0.25,
        0.25
      ],
      [
        0.5,
        0.5
      ],
      [
        0.75,
        0.75
      ],
      [
        1,
        1
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Velocity reduction (m/s) = 0.1. Ideal pressure increment (MPa): 0.1.",
      "Velocity reduction (m/s) = 0.25. Ideal pressure increment (MPa): 0.25.",
      "Velocity reduction (m/s) = 0.5. Ideal pressure increment (MPa): 0.5.",
      "Velocity reduction (m/s) = 0.75. Ideal pressure increment (MPa): 0.75.",
      "Velocity reduction (m/s) = 1. Ideal pressure increment (MPa): 1."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Ideal pressure increment (MPa) without rounding intermediate values.",
        "answer": "1,000 × 1,000 × 0.5 = 500,000 Pa = 0.5 MPa. Ideal pressure increment (MPa) = 0.5. A transient workflow is required for time evolution, reflections and supported boundary behavior."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Velocity reduction (m/s) changes from 0.1 to 1. Other controls remain as stated in the premise. Ideal pressure increment (MPa) changes from 0.1 to 1."
      },
      {
        "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. This is the analytical Joukowsky estimate, not a full closure-time or reflection history. Δv is a positive velocity-reduction magnitude. A transient workflow is required for time evolution, reflections and supported boundary behavior."
      }
    ]
  },
  "recorded": null
}