Verified calculation capability

Trapezoidal alternate depth Calculation Capability

Trapezoid both y from E, Q, b, z with E=y+Q²/(2gA²), A=(b+z y)y. Not rectangular alternate depth, not trapezoid E, not trapezoid yc, not trapezoid yn, not Manning n, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.trapezoid_alternate_depth · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Specific energy

Specific energy: E = y + Q² / (2g A²)
Section: A = (b + z y) y
Critical: Ec = yc + D_c / 2

Solve modes: depths · energy

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/alternate-depth. Do not send a bank angle.	—	input / output
`Q`	Volume flow in m³/s. Required. Alternatives: flow, Q_m3_s.	—	input / output
`E`	Specific energy in m. Required for depths. Alternatives: energy, E_m. Do not send M.	—	input / output
`y`	One flow depth in m. Required for energy. Alternatives: y_m, depth. Do not send y1, y2, yn, or yc.	—	input / output
`g`	Gravity in m/s². Optional; default 9.80665. Alternatives: g_m_s2.	—	input / output
`y_sub`	—	—	output
`y_super`	—	—	output
`y_alt`	—	—	output
`yc`	—	—	output
`Ec`	—	—	output
`A_sub`	—	—	output
`A_super`	—	—	output
`T_sub`	—	—	output
`T_super`	—	—	output
`v_sub`	—	—	output
`v_super`	—	—	output
`Fr_sub`	—	—	output
`Fr_super`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Trapezoid alternate depths: E = y + Q²/(2g A²) with A=(b+z y)y; both y_sub>yc and y_super<yc at the same E, Q, b, z; SI; default g=9.80665; z>0 is run/rise
Unknown is the pair (depths mode) or E (energy invert from one y); E>Ec=yc+D_c/2; Fr is reported not an input
Not rectangular alternate depth; not trapezoid E from y+Q; not trapezoid yc as the product; not trapezoid yn; not Manning n; not Q=Av

Not supported

rectangular alternate depth
trapezoid E from y+Q
trapezoid yc as the product
trapezoid yn
Manning n
Q=Av
z=0

Example

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

E=1.02266 Q=2 b=2 z=1 → y_sub≈1.0000

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-alternate-depth
Engine: trapezoidal-alternate-depth
REST: POST /api/v1/calc/trapezoidal-alternate-depth
MCP: execute_calculation with capability_id: "physics.fluid.trapezoid_alternate_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 — Energy and volume flow
Chow, V.T. Open-Channel Hydraulics — Specific energy and alternate depths 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_alternate_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.