Verified calculation capability

Alternate depth Calculation Capability

Rectangular both y from E, Q, b with E=y+Q²/(2gA²). Not specific energy E from y+v, not specific force M, not hydraulic jump y2, not critical depth yc as the product, not Manning n, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.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 y
Critical: Ec = (3/2) yc

Solve modes: depths · energy

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Rectangular surface width in m. Required. Alternatives: width, b_m, channel_width. Do not send side-weir B.	—	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
`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

Rectangular alternate depths: E = y + Q²/(2g A²) with A=b y; both y_sub>yc and y_super<yc at the same E, Q, b; SI; default g=9.80665
Unknown is the pair (depths mode) or E (energy invert from one y); E>Ec=1.5 yc; Fr is reported not an input
Not specific energy E from y+v; not specific force M; not hydraulic jump y2 from Fr₁>1; not critical-depth yc as the product; not Manning n; not Q=Av

Not supported

specific energy from y+v
specific force M
hydraulic jump y2 from Fr₁>1
critical depth yc as the product
Manning n
Q=Av
trapezoid z

Example

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

E=1.05099 Q=2 b=2 → 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: 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; 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: 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. Production surface contract 1/1.

Tool id: alternate-depth
Engine: alternate-depth
REST: POST /api/v1/calc/alternate-depth
MCP: execute_calculation with capability_id: "physics.fluid.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

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.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.