Public evidence

physics.fluid.pipe_bend

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

16/16 calculation tests · Production surface contract 3/3

Golden tests 2 / 2
Boundary tests 9 / 9
Property tests 5 / 5
Production surface contract 3 / 3
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-17T15:07:30.016Z
Semantic contract PASS
Evidence attested at 2026-09-17T15:07:29.295Z
Last production check 2026-09-17T15:07:29.295Z
Public / cache PASS
Origin PASS
Supplemental domain review Not performed
Named expert review Not performed

release artifacts aligned PASS
schema valid input executes PASS
engine success output 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.

Build & scope

Engine identity and declared limitations.

Tool: pipe-bend
Engine: pipe-bend
Engine build: 2026-09-17
Evidence core: 2026-09-17T13:51:07.147Z
Rendered: 2026-09-17T14:46:34.519Z
Last reviewed: —

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

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

ISO 80000-4 — Mechanics — Length, speed, pressure, plane angle
Supports: h is a head; v is a speed; Δp is a pressure; θ is a plane angle
Idelchik — Handbook of Hydraulic Resistance — Circular-arc bends, B1 at 90°
Supports: ζ_90 = 0.21 / √(R/D) for a circular-arc of circular section in the quadratic region; this page scales linearly with θ/90°

Published checks

Golden, boundary, and property cases included in this evidence build.

ID	Kind	Status	Detail
`golden-pb-h`	golden	pass	Expected h=0.030284026461467467 · v=2 · K=0.14849242404917495 · rd=2 · dP=296.9848480983499 · mode=head · model=circular_arc_bend · Actual mode=head · h=0.030284026461467467 · v=2 · K=0.14849242404917495 · theta=1.5707963267948966 · theta_deg=90 · rd=2 · g=9.80665
`golden-pb-dP`	golden	pass	Expected dP=296.9848480983499 · model=circular_arc_bend · Actual mode=pressure · h=0.030284026461467467 · v=2 · K=0.14849242404917495 · theta=1.5707963267948966 · theta_deg=90 · rd=2 · g=9.80665
`boundary-pb-v`	boundary	pass	Expected v=2 · model=circular_arc_bend · Actual mode=velocity · h=0.030284026461467467 · v=2 · K=0.14849242404917495 · theta=1.5707963267948966 · theta_deg=90 · rd=2 · g=9.80665
`boundary-pb-theta`	boundary	pass	Expected theta_deg=90 · model=circular_arc_bend · Actual mode=angle · h=0.030284026461467467 · v=2 · K=0.14849242404917495 · theta=1.5707963267948966 · theta_deg=90 · rd=2 · g=9.80665
`boundary-pb-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-pb-K`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-pb-Q`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-pb-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-pb-zero`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-pb-rd`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-pb-wide`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`property-pb-h`	property	pass	h=K v²/(2g)
`property-pb-K`	property	pass	K=0.21 (θ/90)/√(R/D)
`property-pb-roundtrip-v`	property	pass	v invert
`property-pb-roundtrip-t`	property	pass	θ invert
`property-pb-model`	property	pass	circular_arc_bend