physics.fluid.pipe_bend

Three distinct suites: educational examples on the calculator page, this legacy regression count (16/16 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. 4/4 golden · 8/8 CVP boundary · 9/9 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract. digest 4fe81755cb43. O2: circular-arc bend K=0.21 (θ/90)/√(R/D) vs a separate-module identity (≤2 ULP). Not minor-loss K given, not mitered, not Darcy, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated pipe-bend vectors. Not minor-loss K given, not mitered, not Darcy, and not Q=Av.

• Golden (oracle-backed) 4 / 4
• CVP boundary 8 / 8
• Invalid input 9 / 9
• Property 1 / 1
• Metamorphic 1 / 1
• O3 high-precision 8 / 8
• Cross-interface 2 / 2
• CVP contract 5 / 5
• 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 v² / (2g) with K = 0.21 (θ/90)/√(R/D), plus pressure, velocity, and angle solves, + O3 mpmath tabulated head.
• Assurance Engineering
• Deferred Not minor-loss K given, not mitered, not Darcy, and not Q=Av.

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

Fingerprint sha256:1d126b6c47b6a579fb15719ef325004c92359151293d5a62d37a69327ef4701e

Input schema sha256:0a606d661a87c0430fd19f9ebfdf04cfaf9876fddb36b89502d46cc2be165fdc · Output schema sha256:681ddc07cc28c0117dd7903081532861b726d1148827ae55f89b68e05db3c92c · 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-bend

Engine

pipe-bend

Engine build

2026-09-17

Evidence core

2026-09-17T13:51:07.147Z

Rendered

2026-11-10T05:18:41.957Z

Last reviewed

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Assumptions

• Circular-arc bend: h = K v² / (2g); K = 0.21 (θ/90)/√(R/D); Idelchik 90° B1 scaled linearly in θ; K is reported, not an input
• Require 0 < θ ≤ 180° and R/D ≥ 1; default g=9.80665 m/s²; default ρ=1000 kg/m³; incompressible
• Not minor-loss K given, not mitered R/D<1, not Darcy f, not orifice C_d, not Q=Av, not gradual contraction α

Limitations

• Circular-arc bend: h = K v² / (2g); K = 0.21 (θ/90)/√(R/D); Idelchik 90° B1 scaled linearly in θ; K is reported, not an input
• Require 0 < θ ≤ 180° and R/D ≥ 1; default g=9.80665; default ρ=1000 for Δp; incompressible
• Not minor-loss K given, not mitered R/D<1, not Darcy f, not orifice C_d, not Q=Av, not gradual contraction α