Verified calculation capability

Critical depth Calculation Capability

Rectangular yc=(q²/g)^{1/3}. Not a Froude wrap, not specific energy, not a hydraulic jump, not Manning, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.critical_depth · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Critical depth

Critical depth: yc = (q² / g)^{1/3}
Unit discharge invert: q = √(g yc³)
From discharge: q = Q / b

Solve modes: depth · unit discharge

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`q`	Unit discharge in m²/s. Required except unit_discharge invert. Alternative: q_m2_s or Q+b.	—	input / output
`q_m2`	Unit discharge in m²/s (query/UI). REST may send q.	s	input
`Q`	Volumetric discharge in m³/s. Use with b as q=Q/b. Do not send with q.	—	input / output
`b`	Rectangular width in m. Required with Q.	—	input / output
`yc`	Critical depth in m. Required for unit_discharge invert. Do not send with depth mode.	—	input / output
`g`	Gravity in m/s². Default 9.80665.	—	input / output
`vc`	—	—	output
`model`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

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

Not supported

Froude-only Fr=v/√(gL)
specific energy E=y+v²/(2g)
hydraulic jump sequent depths
Manning n
Q=Av

Example

One numerical check. The calculator page holds worked steps and FAQ.

q=1 → yc=(1/g)^{1/3}

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 17/17 calculation tests · golden 2/2 · boundary 10/10 · property 5/5
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

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

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 3/3.

Tool id: critical-depth
Engine: critical-depth
REST: POST /api/v1/calc/critical-depth
MCP: execute_calculation with capability_id: "physics.fluid.critical_depth"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 80000-4 — Mechanics — Length, speed, acceleration
Chow, V.T. Open-Channel Hydraulics — Critical flow

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"physics.fluid.critical_depth"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.