Public evidence

physics.fluid.critical_depth

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

17/17 calculation tests · Production surface contract 3/3

Golden tests 2 / 2
Boundary tests 10 / 10
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; 163 CURRENT) @ 2026-09-17T09:03:11.906Z
Semantic contract PASS
Evidence attested at 2026-09-17T09:03:11.074Z
Last production check 2026-09-17T09:03:11.074Z
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 sha256:649c7fa8bd29869eca9c3e854991a768943aa7b9146bc63b206422d3ee53e7e1

Input schema sha256:d49a2eacfe2366fc685869d86c01f1c37d7dd297fd06351f4d8e2465063279d7 · Output schema sha256:abecc9666596c2b02a611a9636356763de9935f68c5547102e1c88f40ad8703e · 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: critical-depth
Engine: critical-depth
Engine build: 2026-09-17
Evidence core: 2026-09-17T08:40:57.187Z
Rendered: 2026-09-17T08:49:50.941Z
Last reviewed: —

Assumptions

Rectangular critical depth: yc = (q²/g)^{1/3}; q = Q/b; default g=9.80665 m/s²
Critical speed vc = √(g yc) is reported, not an input; Fr=1 is the definition, not a Froude wrap
Not a Froude wrap, not specific energy E, not a hydraulic jump, not Manning, not Q=Av

Limitations

Rectangular critical depth: yc = (q²/g)^{1/3}; q = Q/b; default g=9.80665 m/s²
Critical speed vc = √(g yc) is reported, not an input; Fr=1 is the definition, not a Froude wrap
Not a Froude wrap, not specific energy E, not a hydraulic jump, 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 — Length, speed, acceleration
Supports: yc is a length; q is discharge per width; g is acceleration
Chow, V.T. Open-Channel Hydraulics — Critical flow
Supports: yc = (q²/g)^{1/3} for a rectangular channel at Fr=1

Published checks

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

ID	Kind	Status	Detail
`golden-cd-yc`	golden	pass	Expected yc=0.46718953723930495 · q=1 · mode=depth · model=critical_depth · Actual mode=depth · yc=0.46718953723930495 · q=1 · g=9.80665 · vc=2.140458893641228 · model=critical_depth
`golden-cd-q`	golden	pass	Expected q=1 · model=critical_depth · Actual mode=unit_discharge · yc=0.46718953723930495 · q=0.9999999999999999 · g=9.80665 · vc=2.140458893641228 · model=critical_depth
`boundary-cd-Qb`	boundary	pass	Expected yc=0.46718953723930495 · q=1 · model=critical_depth · Actual mode=depth · yc=0.46718953723930495 · q=1 · g=9.80665 · vc=2.140458893641228 · model=critical_depth · Q=2 · b=2
`boundary-cd-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-cd-Fr`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-cd-E`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-cd-y1`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-cd-n`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-cd-A`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-cd-v`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`boundary-cd-froude`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-cd-zero`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`property-cd-yc`	property	pass	yc=(q²/g)^{1/3}
`property-cd-roundtrip-q`	property	pass	q invert
`property-cd-Qb`	property	pass	Q/b
`property-cd-vc`	property	pass	vc=√(g yc)
`property-cd-model`	property	pass	critical_depth