{
  "capability_id": "physics.fluid.pipe_tee",
  "tool_id": "pipe-tee",
  "engine": "pipe-tee",
  "calculation_version": "1.0.0",
  "generated_at": "2026-11-10T05:18:41.961Z",
  "engine_build": "2026-09-24",
  "test_count": 7,
  "passed": 7,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 1,
      "total": 1
    },
    "boundary": {
      "passed": 0,
      "total": 0
    },
    "property": {
      "passed": 6,
      "total": 6
    }
  },
  "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": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/physics/pipe-tee",
  "api": "https://www.calculatorx.com/api/v1/calc/pipe-tee",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.pipe_tee.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.pipe_tee.output.json",
  "assumptions": [
    "Equal-area sharp 90° T: h = K v_c² / (2g); K referenced to common-channel speed; K is reported, not an input",
    "Dividing: branch K=1+q², run K=0.4(1−q)². Combining: branch K=1+q², run K=1.55q−q². q=Q_path/Q_c in [0,1]; default g=9.80665 m/s²; default ρ=1000 kg/m³",
    "Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not a non-90° wye, not Q=Av"
  ],
  "limitations": [
    "Equal-area sharp 90° T: h = K v_c² / (2g); K referenced to common-channel speed; K is reported, not an input",
    "Dividing: branch K=1+q², run K=0.4(1−q)². Combining: branch K=1+q², run K=1.55q−q². q=Q_path/Q_c in [0,1]; default g=9.80665; default ρ=1000 for Δp",
    "Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not a non-90° wye, not Q=Av"
  ],
  "boundary_conditions": [
    "missing v_m_s, h, or q_ratio when required → MISSING_REQUIRED_INPUT",
    "v_m_s ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "q_ratio > 1 or K=0 on velocity invert → VALUE_OUT_OF_RANGE",
    "K, rd, n_miters, θ, α, f, Q, A, v1/v2, ri_d → MIXED_INPUT_ENCODING",
    "flush, circular, or unknown kind/path/mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Length, speed, pressure",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "h is a head; v is a speed; Δp is a pressure",
      "kind": "standard"
    },
    {
      "title": "Idelchik — Handbook of Hydraulic Resistance",
      "section": "Diagrams 7-18 / 7-20 No.1 (dividing) and 7-1 / 7-4 (combining), equal-area 90° T",
      "supports": "Branch K=1+q²; dividing run K=0.4(1−q)²; combining run K=1.55q−q²; K referenced to v_c. Not catalog K, not a bend, not entrance/exit",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:ecce7f401a4da9aac04573a47cf8a80bf6ed4194061ed9cfa08663f759e67cf0",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 7,
      "total": 7,
      "golden": 1,
      "boundary": 0,
      "property": 6
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-24T02:12:38.088Z",
  "rendered_at": "2026-11-10T05:18:41.961Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
      "engine": "1.0.0",
      "page": "1.0.0",
      "capability": "1.0.0",
      "evidence": "1.0.0",
      "input_schema": "1.0.0",
      "output_schema": "1.0.0",
      "mcp_contract": "1.0.0"
    },
    "digests": {
      "input_schema_sha256": "3ed3522dc1f7f22a7988da7fe9016a7b55f737bdb09ece9cd2468d3111d1859f",
      "output_schema_sha256": "fb05c5560318d746eabf56a4fd2799c910f65c7f3cf7af0844862fa41923ce91",
      "evidence_sha256": "d1b055ca9592cfc4e8c5d29f8597bd67be142736a82f9afea235736de6a219b2",
      "evidence_core_sha256": "d1b055ca9592cfc4e8c5d29f8597bd67be142736a82f9afea235736de6a219b2",
      "capability_sha256": "7e559fa82a2a5e3525297e7d606ef32347a4056e770b396443eff91c2907a837",
      "engine_sha256": "c6ebd8436f08b413e1ac6317b2d48550f2e6639a90dff254244e3aa562158b8d",
      "mcp_contract_sha256": "eb3e39ad4a95ed263415b4932f185d5edfe00a2403267b7c5ed5f718d1ff6da3"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  },
  "tests": [],
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}