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  "engine_build": "2026-09-17",
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  "failed": 0,
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    "boundary": {
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  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
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  "reviewer_role": null,
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    "scope": [
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      "assumptions",
      "limitations",
      "sources",
      "tests"
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  "assumptions": [
    "Sharp segmented miter: h = K v² / (2g); K = n [sin²(δ/2) + 2 sin⁴(δ/2)], δ = θ/n; K is reported, not an input",
    "Require n ≥ 1 integer, 0 < θ ≤ 180°, and each miter δ ≤ 90° (n=1 therefore θ ≤ 90°); default g=9.80665 m/s²; default ρ=1000 kg/m³; incompressible",
    "Not circular-arc R/D, not minor-loss K given, not Crane f_T, not Darcy f, not orifice C_d, not Q=Av"
  ],
  "limitations": [
    "Sharp segmented miter: h = K v² / (2g); K = n [sin²(δ/2) + 2 sin⁴(δ/2)], δ = θ/n; K is reported, not an input",
    "Require n ≥ 1 integer, 0 < θ ≤ 180°, and each miter δ ≤ 90° (n=1 therefore θ ≤ 90°); default g=9.80665; default ρ=1000 for Δp; incompressible",
    "Not circular-arc R/D, not minor-loss K given, not Crane f_T, not Darcy f, not orifice C_d, not Q=Av"
  ],
  "boundary_conditions": [
    "missing v_m_s, h, θ, or n_miters when required → MISSING_REQUIRED_INPUT",
    "v_m_s ≤ 0, h ≤ 0, θ ≤ 0, or n_miters ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "non-integer n, each miter > 90°, or θ > 180° → VALUE_OUT_OF_RANGE",
    "K, k, rd, f/f_T/Re, Q, C_d, v1/v2, alpha_deg → MIXED_INPUT_ENCODING",
    "circular, minor, darcy, or orifice as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Length, speed, pressure, plane angle",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "h is a head; v is a speed; Δp is a pressure; θ is a plane angle",
      "kind": "standard"
    },
    {
      "title": "Idelchik — Handbook of Hydraulic Resistance",
      "section": "Sharp-edged / mitered elbows",
      "supports": "Preliminary sharp-miter estimate ζ = sin²(δ/2) + 2 sin⁴(δ/2) per miter; n equal miters sum. Not circular-arc B1, not Crane f_T",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:99f9511326866f2162f5a6a1603582896c69b5adebc5d3e4db16e25ed2dd8fc4",
  "tests": [
    {
      "id": "golden-mit-h",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "v_m_s": 2,
        "theta_deg": 90,
        "n_miters": 1
      },
      "expect": {
        "h": 0.2039432425955856,
        "v": 2,
        "K": 0.9999999999999997,
        "n": 1,
        "dP": 1999.9999999999993,
        "mode": "head",
        "model": "segmented_miter"
      },
      "expectWarning": null,
      "actual": {
        "mode": "head",
        "h": 0.2039432425955856,
        "v": 2,
        "K": 0.9999999999999997,
        "theta": 1.5707963267948966,
        "theta_deg": 90,
        "n": 1,
        "g": 9.80665,
        "rho": 1000,
        "dP": 1999.9999999999993,
        "model": "segmented_miter"
      },
      "tol": 1e-12
    },
    {
      "id": "golden-mit-dP",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "pressure",
        "v_m_s": 2,
        "theta_deg": 90,
        "n_miters": 1
      },
      "expect": {
        "dP": 1999.9999999999993,
        "model": "segmented_miter"
      },
      "expectWarning": null,
      "actual": {
        "mode": "pressure",
        "h": 0.2039432425955856,
        "v": 2,
        "K": 0.9999999999999997,
        "theta": 1.5707963267948966,
        "theta_deg": 90,
        "n": 1,
        "g": 9.80665,
        "rho": 1000,
        "dP": 1999.9999999999993,
        "model": "segmented_miter"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-mit-v",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "velocity",
        "h": 0.2039432425955856,
        "theta_deg": 90,
        "n_miters": 1
      },
      "expect": {
        "v": 2,
        "model": "segmented_miter"
      },
      "expectWarning": null,
      "actual": {
        "mode": "velocity",
        "h": 0.2039432425955856,
        "v": 2,
        "K": 0.9999999999999997,
        "theta": 1.5707963267948966,
        "theta_deg": 90,
        "n": 1,
        "g": 9.80665,
        "rho": 1000,
        "dP": 1999.9999999999993,
        "model": "segmented_miter"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-mit-theta",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "angle",
        "v_m_s": 2,
        "h": 0.2039432425955856,
        "n_miters": 1
      },
      "expect": {
        "theta_deg": 90,
        "model": "segmented_miter"
      },
      "expectWarning": null,
      "actual": {
        "mode": "angle",
        "h": 0.2039432425955856,
        "v": 2,
        "K": 0.9999999999999997,
        "theta": 1.5707963267948963,
        "theta_deg": 89.99999999999999,
        "n": 1,
        "g": 9.80665,
        "rho": 1000,
        "dP": 1999.9999999999993,
        "model": "segmented_miter"
      },
      "tol": 1e-9
    },
    {
      "id": "boundary-mit-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v_m_s": 2,
        "theta_deg": 90
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "n_miters is required"
    },
    {
      "id": "boundary-mit-K",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v_m_s": 2,
        "theta_deg": 90,
        "n_miters": 1,
        "K": 0.9
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Mitered bend does not take minor-loss K. That is /calc/physics/minor-loss. K = n [sin²(δ/2)+2 sin⁴(δ/2)] is reported"
    },
    {
      "id": "boundary-mit-rd",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v_m_s": 2,
        "theta_deg": 90,
        "n_miters": 1,
        "rd": 2
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Mitered bend does not take R/D. Circular-arc is /calc/physics/pipe-bend. Send n_miters"
    },
    {
      "id": "boundary-mit-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v_m_s": 2,
        "theta_deg": 90,
        "n_miters": 1,
        "mode": "circular"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be head|pressure|velocity|angle. Not circular-arc, minor-loss, Darcy, or Q=Av"
    },
    {
      "id": "boundary-mit-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v_m_s": 0,
        "theta_deg": 90,
        "n_miters": 1
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "v_m_s must be greater than zero"
    },
    {
      "id": "boundary-mit-wide",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v_m_s": 2,
        "theta_deg": 91,
        "n_miters": 1
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "Each miter must be ≤ 90°. n=1 is a single miter, so θ ≤ 90°. Use more miters or /calc/physics/pipe-bend"
    },
    {
      "id": "property-mit-h",
      "ok": true,
      "kind": "property",
      "detail": "h=K v²/(2g)",
      "expect": 0.2039432425955856,
      "actual": 0.2039432425955856
    },
    {
      "id": "property-mit-K",
      "ok": true,
      "kind": "property",
      "detail": "K=n [sin²(δ/2)+2 sin⁴(δ/2)]",
      "expect": 0.9999999999999997,
      "actual": 0.9999999999999997
    },
    {
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      "detail": "v invert",
      "expect": 2,
      "actual": 2
    },
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      "kind": "property",
      "detail": "θ invert",
      "expect": 90,
      "actual": 89.99999999999999
    },
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      "ok": true,
      "kind": "property",
      "detail": "segmented_miter",
      "expect": true,
      "actual": "segmented_miter"
    }
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