physics.fluid.pipe_tee

Three distinct suites: educational examples on the calculator page, this legacy regression count (7/7 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-26.o2-o3. Calculation version 1.0.0. CVP 1.0.0-proposed. 5/5 golden · 1/1 CVP boundary · 2/2 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract. digest 8a55d3597732. O2: equal-area 90° T K vs a separate-module identity (≤2 ULP). Not catalog K, not circular-arc R/D, not mitered n, not entrance/exit, not a non-90° wye, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated pipe-tee vectors. Not catalog K, not circular-arc R/D, not mitered n, not entrance/exit, not a non-90° wye, and not Q=Av.

• Golden (oracle-backed) 5 / 5
• CVP boundary 1 / 1
• Invalid input 2 / 2
• Property 1 / 1
• Metamorphic 1 / 1
• O3 high-precision 8 / 8
• Cross-interface 2 / 2
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
• Verified scope h = K v_c² / (2g) for equal-area 90° T; dividing branch 1+q², dividing run 0.4(1−q)², combining branch 1+q², combining run q(1.55−q); plus pressure and velocity solves; + O3 mpmath tabulated head.
• Assurance Engineering
• Deferred Not catalog K given, not circular-arc R/D, not mitered n, not entrance/exit geometry, not a non-90° wye, and not Q=Av.

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:ecce7f401a4da9aac04573a47cf8a80bf6ed4194061ed9cfa08663f759e67cf0

Input schema sha256:3ed3522dc1f7f22a7988da7fe9016a7b55f737bdb09ece9cd2468d3111d1859f · Output schema sha256:fb05c5560318d746eabf56a4fd2799c910f65c7f3cf7af0844862fa41923ce91 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

pipe-tee

Engine

pipe-tee

Engine build

2026-09-24

Evidence core

2026-09-24T02:12:38.088Z

Rendered

2026-11-10T05:18:41.961Z

Last reviewed

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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