{
  "capability_id": "physics.fluid.manning",
  "tool_id": "manning-formula",
  "engine": "manning-formula",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-17T02:45:35.817Z",
  "engine_build": "2026-09-17",
  "test_count": 13,
  "passed": 13,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 1,
      "passed": 1
    },
    "boundary": {
      "total": 7,
      "passed": 7
    },
    "property": {
      "total": 5,
      "passed": 5
    }
  },
  "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/manning-formula",
  "api": "https://www.calculatorx.com/api/v1/calc/manning-formula",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.manning.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.manning.output.json",
  "assumptions": [
    "SI Manning k=1",
    "Uniform open-channel flow",
    "R = A/P",
    "Not Q=Av identities",
    "Not Darcy–Weisbach",
    "Not a weir"
  ],
  "limitations": [
    "SI only: k=1. US customary 1.486 is out of scope",
    "Uniform open-channel flow; R=A/P",
    "Not Q=Av identities (see /calc/physics/flow-rate)",
    "Not Darcy–Weisbach pipe head loss",
    "Not a weir or orifice"
  ],
  "boundary_conditions": [
    "missing n, A, R/P, or S when required → MISSING_REQUIRED_INPUT",
    "n, A, R, P, S, or Q ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "R and P together → MIXED_INPUT_ENCODING",
    "k given and k ≠ 1 → INVALID_MODE",
    "weir is not a mode on this page"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Volume flow rate and hydraulic radius",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "Q is volume flow; hydraulic radius R = A/P",
      "kind": "standard"
    },
    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Manning formula",
      "supports": "SI form Q = (1/n) A R^{2/3} S^{1/2} for uniform flow",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:93f113a7fd2df34c77ef3cca909a6174552c51fc00e487ead910dbe897194904",
  "tests": [
    {
      "id": "golden-manning",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "n": 0.013,
        "A": 1,
        "R": 0.5,
        "S": 0.001
      },
      "expect": {
        "Q": 1.532392380637864,
        "v": 1.532392380637864,
        "n": 0.013,
        "A": 1,
        "R": 0.5,
        "S": 0.001,
        "k": 1,
        "model": "manning"
      },
      "expectWarning": null,
      "actual": {
        "mode": "discharge",
        "Q": 1.532392380637864,
        "v": 1.532392380637864,
        "n": 0.013,
        "A": 1,
        "R": 0.5,
        "S": 0.001,
        "k": 1,
        "model": "manning"
      },
      "tol": 1e-10
    },
    {
      "id": "boundary-manning-p",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "n": 0.013,
        "A": 1,
        "P": 2,
        "S": 0.001
      },
      "expect": {
        "R": 0.5,
        "model": "manning"
      },
      "expectWarning": null,
      "actual": {
        "mode": "discharge",
        "Q": 1.532392380637864,
        "v": 1.532392380637864,
        "n": 0.013,
        "A": 1,
        "R": 0.5,
        "S": 0.001,
        "k": 1,
        "model": "manning"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-manning-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "n",
        "Q": 1.532392380637864,
        "A": 1,
        "R": 0.5,
        "S": 0.001
      },
      "expect": {
        "n": 0.013,
        "model": "manning"
      },
      "expectWarning": null,
      "actual": {
        "mode": "n",
        "Q": 1.532392380637864,
        "v": 1.532392380637864,
        "n": 0.013000000000000003,
        "A": 1,
        "R": 0.5,
        "S": 0.001,
        "k": 1,
        "model": "manning"
      },
      "tol": 1e-10
    },
    {
      "id": "boundary-manning-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "A": 1,
        "R": 0.5,
        "S": 0.001
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "n is required"
    },
    {
      "id": "boundary-manning-n0",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "n": 0,
        "A": 1,
        "R": 0.5,
        "S": 0.001
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "n must be greater than zero"
    },
    {
      "id": "boundary-manning-mixed",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "n": 0.013,
        "A": 1,
        "R": 0.5,
        "S": 0.001,
        "P": 2
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Use R or A+P, not both encodings"
    },
    {
      "id": "boundary-manning-k",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "n": 0.013,
        "A": 1,
        "R": 0.5,
        "S": 0.001,
        "k": 1.486
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "SI Manning only (k=1). US customary 1.486 is out of scope"
    },
    {
      "id": "boundary-manning-weir",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "n": 0.013,
        "A": 1,
        "R": 0.5,
        "S": 0.001,
        "mode": "weir"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be discharge|velocity|n|slope"
    },
    {
      "id": "property-manning-v",
      "ok": true,
      "kind": "property",
      "detail": "V=(1/n)R^{2/3}S^{1/2}",
      "expect": 1.532392380637864,
      "actual": 1.532392380637864
    },
    {
      "id": "property-manning-q",
      "ok": true,
      "kind": "property",
      "detail": "Q=AV from Manning V",
      "expect": 1.532392380637864,
      "actual": 1.532392380637864
    },
    {
      "id": "property-manning-r",
      "ok": true,
      "kind": "property",
      "detail": "R=A/P",
      "expect": 0.5,
      "actual": 0.5
    },
    {
      "id": "property-manning-n",
      "ok": true,
      "kind": "property",
      "detail": "n round-trip",
      "expect": 0.013,
      "actual": 0.013000000000000003
    },
    {
      "id": "property-manning-model",
      "ok": true,
      "kind": "property",
      "detail": "manning SI k=1",
      "expect": true,
      "actual": "manning"
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 13,
      "total": 13,
      "golden": 1,
      "boundary": 7,
      "property": 5
    },
    "contract_checks": {
      "passed": 3,
      "total": 3
    }
  },
  "evidence_core_generated_at": "2026-09-17T01:17:06.750Z",
  "rendered_at": "2026-09-17T02:45:35.817Z",
  "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": "ce75b3f712d318b9be8b796e369ab70b38e9ae1e2beb31e450bd3d90afb698a4",
      "output_schema_sha256": "1fb3e4b2796c9eca80d859ad82e7749283a0367586f02b6a82a2c52f47694d62",
      "evidence_sha256": "92e97dc6ef6f55ddbafd241629b326fe8f5d2e53f7010536057d2287bc21e254",
      "evidence_core_sha256": "92e97dc6ef6f55ddbafd241629b326fe8f5d2e53f7010536057d2287bc21e254",
      "capability_sha256": "b76e616e4bc67995eb81beaedfea35b2b1386609302f8aab37c0489c6fcb7132",
      "engine_sha256": "a3e8effccaf4677aec4d1da78c13b5dc595ff97e52b074d5de5ab5cb5a87b094",
      "mcp_contract_sha256": "a942c221699a25eb2b10fc462c0b321092558cb5ffda32cf521d31ee83e3fe87"
    },
    "contract_checks": {
      "total": 3,
      "passed": 3,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}