Verified calculation capability

Trapezoidal critical depth Calculation Capability

Trapezoid Fr=1 from Q, b, z with Q² T = g A³, A=(b+z y)y, T=b+2 z y. Not rectangular yc=(q²/g)^{1/3}, not yn, not E, not Manning Q, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.trapezoid_critical_depth · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Critical condition

Critical condition: Q² T = g A³
Area: A = (b + z y) y
Top width: T = b + 2 z y

Solve modes: depth · discharge

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Bottom width in m. Required. Alternatives: width, b_m, channel_width. Do not send side-weir B.	—	input / output
`z`	Side slope run/rise (z>0). Required. Alternatives: z_side, side_slope, m. z=0 is rectangular /calc/physics/critical-depth. Do not send a bank angle.	—	input / output
`Q`	Volume flow in m³/s. Required for depth. Alternatives: flow, Q_m3_s. Do not send rectangular q.	—	input / output
`yc`	Critical depth in m. Required for discharge. Alternatives: y_c. Do not send with depth mode.	—	input / output
`g`	Gravity in m/s². Optional; default 9.80665. Alternatives: g_m_s2.	—	input / output
`A`	—	—	output
`T`	temperature	—	output
`D`	—	—	output
`P`	—	—	output
`R`	—	—	output
`vc`	—	—	output
`Fr`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Trapezoid critical depth: Fr=1 with A=(b+z yc) yc and T=b+2 z yc so Q² T = g A³; SI; default g=9.80665; z>0 is run/rise
Critical speed vc = Q/A = √(g A/T) is reported, not an input; Fr=1 is the definition, not a Froude wrap
Not rectangular yc=(q²/g)^{1/3}; not normal-depth yn; not specific energy E; not Manning n; not Q=Av

Not supported

rectangular yc=(q²/g)^{1/3}
normal-depth yn
specific energy E
Manning n
Q=Av
z=0

Example

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

Q=2 b=2 z=1 → yc≈0.43298 m

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: 5/5 calculation tests · golden 0/0 · boundary 0/0 · 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: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T21:41:56.329Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T21:41:55.460Z
Last production check: 2026-09-18T21:41:55.460Z
Public / cache: —
Origin: —

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. Production surface contract 1/1.

Tool id: trapezoidal-critical-depth
Engine: trapezoidal-critical-depth
REST: POST /api/v1/calc/trapezoidal-critical-depth
MCP: execute_calculation with capability_id: "physics.fluid.trapezoid_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 in a trapezoidal section

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.trapezoid_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.