Public evidence

physics.fluid.hazen_williams

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

17/17 calculation tests · Production surface contract 4/4

Golden tests 2 / 2
Boundary tests 10 / 10
Property tests 5 / 5
Production surface contract 4 / 4
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; 163 CURRENT) @ 2026-09-17T06:27:56.932Z
Semantic contract PASS
Evidence attested at 2026-09-17T06:27:56.176Z
Last production check 2026-09-17T06:27:56.176Z
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
schema rejects incomplete input PASS

Fingerprint sha256:d408aa5ed3f1e0fa778bb51ce68fefeb2a63dd1d69468db502bd68867c116c51

Input schema sha256:1ba406f7d6fa954f4e1167326caf3a5e5413a77d4616742d63a9e3e51cf6cb25 · Output schema sha256:63a1653c24addc4ac4815a5458b81ac356d07614b73de617595f162be7a86808 · 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: hazen-williams
Engine: hazen-williams
Engine build: 2026-09-17
Evidence core: 2026-09-17T04:33:23.369Z
Rendered: 2026-09-17T06:35:12.146Z
Last reviewed: —

Assumptions

SI Hazen–Williams k=10.67
Circular full-flow water pipe
Empirical C; not Darcy f, not Colebrook, not Manning n
Not Q=Av identities
Not US customary gpm/in

Limitations

SI Hazen–Williams: hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87})
Circular full-flow water pipe; empirical C; k=10.67; not US gpm/in
Not Darcy–Weisbach, not Colebrook, not Manning, not Q=Av

Sources

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

ISO 80000-4 — Mechanics — Volume flow rate and hydraulic head
Supports: Q is volume flow; hf is a length of hydraulic head
Williams, G.S. and Hazen, A. Hydraulic Tables — Empirical pipe formula
Supports: Hazen–Williams C correlation for water pipes; SI form uses k=10.67 with Q in m³/s and D in m

Published checks

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

ID	Kind	Status	Detail
`golden-hw-hf`	golden	pass	Expected hf=0.27227779496920657 · Q=0.02 · C=120 · L=100 · D=0.2 · k=10.67 · mode=head_loss · model=hazen_williams · Actual mode=head_loss · hf=0.27227779496920657 · Q=0.02 · v=0.6366197723675813 · C=120 · L=100 · D=0.2 · A=0.031415926535897934
`golden-hw-flow`	golden	pass	Expected Q=0.02 · hf=0.27227779496920657 · model=hazen_williams · Actual mode=flow · hf=0.27227779496920657 · Q=0.020000000000000004 · v=0.6366197723675814 · C=120 · L=100 · D=0.2 · A=0.031415926535897934
`boundary-hw-diameter`	boundary	pass	Expected D=0.2 · model=hazen_williams · Actual mode=diameter · hf=0.27227779496920657 · Q=0.02 · v=0.6366197723675813 · C=120 · L=100 · D=0.2 · A=0.031415926535897934
`boundary-hw-c`	boundary	pass	Expected C=120 · model=hazen_williams · Actual mode=C · hf=0.27227779496920657 · Q=0.02 · v=0.6366197723675813 · C=119.99999999999999 · L=100 · D=0.2 · A=0.031415926535897934
`boundary-hw-slope`	boundary	pass	Expected Q=0.02 · model=hazen_williams · Actual mode=flow · hf=0.27227779496920657 · Q=0.020000000000000004 · v=0.6366197723675814 · C=120 · L=100 · D=0.2 · A=0.031415926535897934
`boundary-hw-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-hw-c0`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-hw-f`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-hw-n`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-hw-v`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-hw-darcy`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-hw-k`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`property-hw-hf`	property	pass	SI k=10.67 hf
`property-hw-s`	property	pass	S=hf/L
`property-hw-roundtrip-q`	property	pass	flow invert Q
`property-hw-length`	property	pass	hf ∝ L
`property-hw-model`	property	pass	hazen_williams