{
  "capability_id": "physics.fluid.pipe_period",
  "tool_id": "pipe-period",
  "engine": "pipe-period",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-17T12:57:09.948Z",
  "engine_build": "2026-09-17",
  "test_count": 17,
  "passed": 17,
  "failed": 0,
  "tests_summary": {
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      "total": 2,
      "passed": 2
    },
    "boundary": {
      "total": 10,
      "passed": 10
    },
    "property": {
      "total": 5,
      "passed": 5
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  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
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      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
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    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
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    "reviewer": null
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  "page": "https://www.calculatorx.com/calc/physics/pipe-period",
  "api": "https://www.calculatorx.com/api/v1/calc/pipe-period",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.pipe_period.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.pipe_period.output.json",
  "assumptions": [
    "Pipe period T = 2L/c; c is a given celerity, not Korteweg–Hall from K, D, e, E",
    "Sudden-closure Joukowsky applies when valve time t < T; this page computes T, not Δp",
    "Not Joukowsky Δp=ρcΔv, not Darcy f, not minor-loss K, not Q=Av"
  ],
  "limitations": [
    "Pipe period T = 2L/c; c is a given celerity, not Korteweg–Hall from K, D, e, E",
    "Sudden-closure Joukowsky applies when valve time t < T; this page computes T, not Δp",
    "Not Joukowsky Δp=ρcΔv, not Darcy f, not minor-loss K, not Q=Av"
  ],
  "boundary_conditions": [
    "missing L, c, or T when required → MISSING_REQUIRED_INPUT",
    "L, c, or T ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "dP/dV/ρ, K/D/e/E, f/Re, n, A/Q, v → MIXED_INPUT_ENCODING",
    "joukowsky, hall, or darcy as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Length, time, speed",
      "supports": "L is a length; T is a time; c is a speed",
      "kind": "standard"
    },
    {
      "title": "Wylie, E.B. and Streeter, V.L. Fluid Transients",
      "section": "Pipe period 2L/a",
      "supports": "T=2L/c is the round-trip time that distinguishes sudden from gradual closure",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:5caa9d568ab44761d7d2fc17815fe60a4359cac980c5881ffe6b64d22ab80e1b",
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      "ok": true,
      "kind": "golden",
      "inputs": {
        "L": 1000,
        "c": 1000
      },
      "expect": {
        "T": 2,
        "L": 1000,
        "c": 1000,
        "mode": "period",
        "model": "pipe_period"
      },
      "expectWarning": null,
      "actual": {
        "mode": "period",
        "T": 2,
        "L": 1000,
        "c": 1000,
        "model": "pipe_period"
      },
      "tol": 1e-12
    },
    {
      "id": "golden-pp-L",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "length",
        "T": 2,
        "c": 1000
      },
      "expect": {
        "L": 1000,
        "model": "pipe_period"
      },
      "expectWarning": null,
      "actual": {
        "mode": "length",
        "T": 2,
        "L": 1000,
        "c": 1000,
        "model": "pipe_period"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pp-c",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "celerity",
        "T": 2,
        "L": 1000
      },
      "expect": {
        "c": 1000,
        "model": "pipe_period"
      },
      "expectWarning": null,
      "actual": {
        "mode": "celerity",
        "T": 2,
        "L": 1000,
        "c": 1000,
        "model": "pipe_period"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pp-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "c is required"
    },
    {
      "id": "boundary-pp-dP",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 1000,
        "dP": 1000000
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pipe period does not take Joukowsky Δp, Δv, or ρ. That is /calc/physics/water-hammer"
    },
    {
      "id": "boundary-pp-K",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 1000,
        "K": 2200000000
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pipe period does not take K, D, e, or E. Give c; wave speed is /calc/physics/wave-celerity"
    },
    {
      "id": "boundary-pp-f",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 1000,
        "f": 0.02
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pipe period does not take Darcy f, Re, or minor-loss K"
    },
    {
      "id": "boundary-pp-A",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 1000,
        "A": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pipe period does not take Q=Av A/Q"
    },
    {
      "id": "boundary-pp-v",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 1000,
        "v": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pipe period uses c, not v. That is /calc/physics/pitot-tube"
    },
    {
      "id": "boundary-pp-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 1000,
        "n": 0.013
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Pipe period does not take Manning n or Chezy C/R/S"
    },
    {
      "id": "boundary-pp-jouk",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 1000,
        "mode": "joukowsky"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be period|length|celerity. Not Joukowsky, Hall, Darcy, or Q=Av"
    },
    {
      "id": "boundary-pp-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1000,
        "c": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "c must be greater than zero"
    },
    {
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      "ok": true,
      "kind": "property",
      "detail": "T=2L/c",
      "expect": 2,
      "actual": 2
    },
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      "id": "property-pp-roundtrip-L",
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      "kind": "property",
      "detail": "L invert",
      "expect": 1000,
      "actual": 1000
    },
    {
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      "kind": "property",
      "detail": "c invert",
      "expect": 1000,
      "actual": 1000
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    {
      "id": "property-pp-double",
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      "kind": "property",
      "detail": "T=2 at L=c=1000",
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      "ok": true,
      "kind": "property",
      "detail": "pipe_period",
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      "actual": "pipe_period"
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      "boundary": 10,
      "property": 5
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