Verified calculation capability

Sudden expansion Calculation Capability

Borda–Carnot h=(v1−v2)²/(2g). Not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.sudden_expansion · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Head loss

Head loss: h = (v1 − v2)² / (2g)
Loss coefficient: K = (1 − v2/v1)²
Pressure drop: Δp = ρ (v1 − v2)² / 2
Downstream area: A2 = A1 / (1 − √(2 g h) / v1)

Solve modes: head · pressure · velocity · area

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`v1`	Upstream speed in m/s. Alternative: v1_m_s.	—	input / output
`v1`	Upstream speed in m/s (query/UI). REST may send v1.	m/s	input
`v2`	Downstream speed in m/s. Required except velocity and area invert. Alternative: v2_m_s.	—	input / output
`v2`	Downstream speed in m/s (query/UI). REST may send v2.	m/s	input
`h`	Head loss in m. Required for velocity and area invert. Alternatives: hm, h_m.	—	input / output
`h`	Head loss in m (query/UI). REST may send h.	m	input
`A1`	Upstream area in m². Required for area invert.	—	input / output
`rho`	Density in kg/m³. Optional; default 1000.	—	input / output
`g`	Gravity in m/s². Optional; default 9.80665.	—	input / output
`K`	—	—	output
`dP`	—	—	output
`A2`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Borda–Carnot sudden expansion: h = (v1 − v2)² / (2g); K = (1 − v2/v1)² is reported, not an input
Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ (v1−v2)² / 2; incompressible; A2 > A1
Not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av, not sudden contraction

Not supported

catalog minor-loss K
Darcy f
orifice C_d
Q=Av
sudden contraction

Example

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

v1=2 v2=1 → h=1/(2g) K=0.25

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) @ 2026-09-17T13:12:27.589Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T13:12:26.751Z
Last production check: 2026-09-17T13:12:26.751Z
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: sudden-expansion
Engine: sudden-expansion
REST: POST /api/v1/calc/sudden-expansion
MCP: execute_calculation with capability_id: "physics.fluid.sudden_expansion"
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, pressure
Borda–Carnot equation — Sudden enlargement

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.sudden_expansion"}}}'

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