physics.fluid.critical_depth

Three distinct suites: educational examples on the calculator page, this legacy regression count (17/17 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.iface. Calculation version 1.0.0. CVP 1.0.0-proposed. 4/4 golden · 10/10 CVP boundary · 11/11 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract. digest 5c7c205b89d1. O2: yc=(q²/g)^{1/3} vs a separate-module identity (≤2 ULP). Not trapezoid critical depth, not alternate depth, not Manning, and not Q=Av alone. ≤2 ULP vs O3 applies only to the published tabulated critical-depth vectors. Not trapezoid yc, not Manning, and not alternate depth.

• Golden (oracle-backed) 4 / 4
• CVP boundary 10 / 10
• Invalid input 11 / 11
• 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 Rectangular yc = (q²/g)^{1/3} with unit-discharge invert; + O3 mpmath tabulated yc.
• Assurance Engineering
• Deferred Not trapezoid critical depth, not alternate depth, not Manning yn, and not Q=Av alone.

• 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 sha256:649c7fa8bd29869eca9c3e854991a768943aa7b9146bc63b206422d3ee53e7e1

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.

Tool

critical-depth

Engine

critical-depth

Engine build

2026-09-18

Evidence core

2026-09-18T22:05:44.918Z

Rendered

2026-11-10T05:18:41.945Z

Last reviewed

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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