{
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    "boundary": {
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  "review_kind": null,
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      "sources",
      "tests"
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  "assumptions": [
    "Korteweg–Hall wave celerity: c = √[(K/ρ)/(1+(K D)/(E e))]; default ρ=1000 kg/m³; thin wall; ψ=1",
    "K is fluid bulk modulus, E is wall Young’s modulus; not Joukowsky Δp=ρcΔv",
    "Not Darcy f, not minor-loss K, not Q=Av, not Y=(F/A)/(ΔL/L0)"
  ],
  "limitations": [
    "Korteweg–Hall wave celerity: c = √[(K/ρ)/(1+(K D)/(E e))]; default ρ=1000 kg/m³; thin wall; ψ=1",
    "K is fluid bulk modulus, E is wall Young’s modulus; not Joukowsky Δp=ρcΔv",
    "Not Darcy f, not minor-loss K, not Q=Av, not Y=(F/A)/(ΔL/L0)"
  ],
  "boundary_conditions": [
    "missing K, D, e, E, or c when required → MISSING_REQUIRED_INPUT",
    "K, D, e, E, c, or ρ ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "c ≥ √(K/ρ) on E invert, or c ≥ √(E e/(ρ D)) on K invert → VALUE_OUT_OF_RANGE",
    "dP/dV, f/Re, K_loss, n, A/Q, v, L, ψ → MIXED_INPUT_ENCODING",
    "joukowsky, darcy, or minor as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Pressure, density, speed, modulus",
      "supports": "K and E are moduli; ρ is a density; c is a speed; D and e are lengths",
      "kind": "standard"
    },
    {
      "title": "Wylie, E.B. and Streeter, V.L. Fluid Transients",
      "section": "Wave speed in a liquid-filled elastic pipe",
      "supports": "c = √[(K/ρ)/(1+(K/E)(D/e))] for a thin-wall line with restraint factor 1",
      "kind": "reference"
    }
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  "fingerprint": "sha256:dfcffb8e60b5a388665e4e0f26e0d90f8eeb99ee7b25e345de0f1e39e98710af",
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      "ok": true,
      "kind": "golden",
      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000
      },
      "expect": {
        "c": 1023.5326314383179,
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "rho": 1000,
        "mode": "celerity",
        "model": "korteweg_hall"
      },
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      "actual": {
        "mode": "celerity",
        "c": 1023.5326314383179,
        "rho": 1000,
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "model": "korteweg_hall"
      },
      "tol": 1e-12
    },
    {
      "id": "golden-wc-K",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "bulk",
        "c": 1023.5326314383179,
        "D": 1,
        "e": 0.01,
        "E": 200000000000
      },
      "expect": {
        "K": 2200000000,
        "model": "korteweg_hall"
      },
      "expectWarning": null,
      "actual": {
        "mode": "bulk",
        "c": 1023.5326314383179,
        "rho": 1000,
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "model": "korteweg_hall"
      },
      "tol": 1e-12
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    {
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        "c": 1023.5326314383179,
        "K": 2200000000,
        "D": 1,
        "e": 0.01
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      "expect": {
        "E": 200000000000,
        "model": "korteweg_hall"
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      "actual": {
        "mode": "youngs",
        "c": 1023.5326314383179,
        "rho": 1000,
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 199999999999.99997,
        "model": "korteweg_hall"
      },
      "tol": 1e-12
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    {
      "id": "boundary-wc-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "K": 2200000000,
        "D": 1
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      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "e is required"
    },
    {
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      "ok": true,
      "kind": "boundary",
      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "dP": 1000000
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Wave celerity does not take Joukowsky Δp or Δv. That is /calc/physics/water-hammer"
    },
    {
      "id": "boundary-wc-f",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "f": 0.02
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Wave celerity does not take Darcy f, Re, or roughness. That is /calc/physics/darcy-weisbach or /calc/physics/colebrook"
    },
    {
      "id": "boundary-wc-Kloss",
      "ok": true,
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      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "K_loss": 0.5
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Wave celerity K is bulk modulus, not minor-loss K. That is /calc/physics/minor-loss"
    },
    {
      "id": "boundary-wc-A",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "A": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Wave celerity does not take Q=Av A/Q"
    },
    {
      "id": "boundary-wc-v",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "v": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Wave celerity uses c, not v. That is /calc/physics/pitot-tube"
    },
    {
      "id": "boundary-wc-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "n": 0.013
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Wave celerity does not take Manning n or Chezy C/R/S"
    },
    {
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      "ok": true,
      "kind": "boundary",
      "inputs": {
        "K": 2200000000,
        "D": 1,
        "e": 0.01,
        "E": 200000000000,
        "mode": "joukowsky"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be celerity|bulk|youngs. Not Joukowsky, Darcy, minor-loss, or Q=Av"
    },
    {
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        "D": 1,
        "e": 0.01,
        "E": 0
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      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "E must be greater than zero"
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      "ok": true,
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      "expect": 1023.5326314383179,
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      "ok": true,
      "kind": "property",
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      "actual": 2200000000
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      "detail": "E invert",
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    },
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      "ok": true,
      "kind": "property",
      "detail": "ρ default 1000",
      "expect": 1000,
      "actual": 1000
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      "ok": true,
      "kind": "property",
      "detail": "korteweg_hall",
      "expect": true,
      "actual": "korteweg_hall"
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