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  "assumptions": [
    "Laminar Hagen–Poiseuille: Q = π Δp D⁴ / (128 μ L); circular, fully developed, Newtonian",
    "Mean speed v = 4Q/(π D²) is reported, not an input",
    "Not Darcy f, not Colebrook, not Q=Av, not Manning"
  ],
  "limitations": [
    "Laminar Hagen–Poiseuille: Q = π Δp D⁴ / (128 μ L); circular, fully developed, Newtonian",
    "Mean speed v = 4Q/(π D²) is reported, not an input",
    "Not Darcy f, not Colebrook, not Q=Av, not Manning"
  ],
  "boundary_conditions": [
    "missing Δp, Q, D, μ, or L when required → MISSING_REQUIRED_INPUT",
    "Δp, Q, D, μ, or L ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "f/Re/ε, n, A/v, K/Cd → MIXED_INPUT_ENCODING",
    "darcy, colebrook, reynolds, or manning as mode → INVALID_MODE"
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  "sources": [
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      "title": "ISO 80000-4 — Mechanics",
      "section": "Dynamic viscosity",
      "supports": "μ has dimension pressure × time; Q volume/time; D and L length; Δp pressure",
      "kind": "standard"
    },
    {
      "title": "White, F.M. Fluid Mechanics",
      "section": "Hagen–Poiseuille flow",
      "supports": "Fully developed laminar flow in a circular tube Q = π Δp D⁴ / (128 μ L)",
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        "D": 0.002,
        "L": 1,
        "mu": 0.001
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        "Q": 3.9269908169872417e-7,
        "dP": 1000,
        "D": 0.002,
        "mode": "flow",
        "model": "poiseuille"
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      "actual": {
        "mode": "flow",
        "Q": 3.9269908169872417e-7,
        "dP": 1000,
        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "v": 0.125,
        "model": "poiseuille"
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        "D": 0.002,
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        "mu": 0.001
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        "model": "poiseuille"
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        "Q": 3.9269908169872417e-7,
        "dP": 999.9999999999999,
        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "v": 0.125,
        "model": "poiseuille"
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        "model": "poiseuille"
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        "Q": 3.9269908169872417e-7,
        "dP": 1000,
        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "v": 0.125,
        "model": "poiseuille"
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      "inputs": {
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        "Q": 3.9269908169872417e-7,
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        "D": 0.002,
        "L": 1
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        "model": "poiseuille"
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      "actual": {
        "mode": "viscosity",
        "Q": 3.9269908169872417e-7,
        "dP": 1000,
        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "v": 0.125,
        "model": "poiseuille"
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      "tol": 1e-12
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    {
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      "ok": true,
      "kind": "boundary",
      "inputs": {
        "D": 0.002,
        "L": 1,
        "mu": 0.001
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      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "dP is required"
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    {
      "id": "boundary-hp-zero",
      "ok": true,
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      "inputs": {
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        "D": 0,
        "L": 1,
        "mu": 0.001
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      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "D must be greater than zero"
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    {
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      "ok": true,
      "kind": "boundary",
      "inputs": {
        "dP": 1000,
        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "f": 0.03
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      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Hagen–Poiseuille does not take Darcy f, Reynolds Re, or Colebrook ε/rel_roughness"
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    {
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      "kind": "boundary",
      "inputs": {
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        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "Re": 200
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      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Hagen–Poiseuille does not take Darcy f, Reynolds Re, or Colebrook ε/rel_roughness"
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      "ok": true,
      "kind": "boundary",
      "inputs": {
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        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "n": 0.013
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      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Hagen–Poiseuille does not take Manning n or Chezy C/R/S"
    },
    {
      "id": "boundary-hp-A",
      "ok": true,
      "kind": "boundary",
      "inputs": {
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        "D": 0.002,
        "L": 1,
        "mu": 0.001,
        "A": 1
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      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Hagen–Poiseuille does not take Q=Av A/v. Mean speed is reported from Q and D"
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      "ok": true,
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        "L": 1,
        "mu": 0.001,
        "eps_m": 0.00001
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      "inputs": {
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        "D": 0.002,
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        "mu": 0.001,
        "mode": "darcy"
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      "expectError": "INVALID_MODE",
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      "ok": true,
      "kind": "property",
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      "expect": 0.125,
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      "kind": "property",
      "detail": "Δp invert",
      "expect": 1000,
      "actual": 999.9999999999999
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      "kind": "property",
      "detail": "D invert",
      "expect": 0.002,
      "actual": 0.002
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      "ok": true,
      "kind": "property",
      "detail": "poiseuille",
      "expect": true,
      "actual": "poiseuille"
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      "golden": 2,
      "boundary": 10,
      "property": 5
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