Verified calculation capability

ISO 5167 long-radius nozzle Calculation Capability

ISO 5167-3 long-radius nozzle Q=C E A2 √(2Δp/ρ) with C=0.9965−0.00653 β^{0.5}. Not ISA 1932, not given C_d=0.98, not RHG orifice, not ISO 5167-4 type C, not Q=Av, not Darcy. · Physics · Fluid

Capability ID physics.fluid.long_radius_nozzle · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Discharge

Discharge: Q = C E A2 √(2Δp / ρ)
Approach: β = D2/D1 · E = 1/√(1 − β⁴)
Long-radius C: C = 0.9965 − 0.00653 β^{0.5}

Solve modes: flow · pressure · coefficient

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`D1`	Inlet diameter in m. Required. Envelope [50 mm, 630 mm]. Alternative: D_inlet. Do not send orifice D+d.	—	input / output
`D2`	Throat diameter in m. Required unless beta. Alternative: D_throat. Do not mix with beta.	—	input / output
`beta`	D2/D1. Alternative to D2. Alternative: diameter_ratio. Envelope [0.20, 0.80].	—	input / output
`Re_D`	Pipe Reynolds number on D1. Required as the ISO envelope [1e4, 1e7], not a term in C. Alternatives: Re, ReD. Do not send ρ, μ, v.	—	input / output
`dP`	Inlet-to-throat differential pressure in Pa. Required for flow. Alternatives: deltaP, dP_Pa, dp.	—	input / output
`rho`	Density in kg/m³. Required for flow and pressure.	—	input / output
`Q`	Volume flow in m³/s. Required for pressure invert. Alternative: flow, Q_m3_s.	—	input / output
`E`	—	—	output
`A1`	—	—	output
`A2`	—	—	output
`C`	—	—	output
`Cd`	—	—	output
`v1`	—	—	output
`v2`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

ISO 5167-3 long-radius nozzle: Q = C E A2 √(2Δp/ρ); C = 0.9965 − 0.00653 β^{0.5}; incompressible ε=1; C is reported, not an input
C from β, not Re_D; Re_D∈[1e4,1e7] is the ISO envelope; β∈[0.20,0.80]; D∈[50 mm, 630 mm]
Not ISA 1932 C(β,Re), not given C_d=0.98, not RHG orifice, not ISO 5167-4 type C, not Q=Av, not Darcy f, not compressible ε

Not supported

ISA 1932 C(β
Re)
given C_d=0.98
RHG orifice
ISO 5167-4 type C
Q=Av
Darcy f
compressible ε

Example

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

D1=0.1 D2=0.05 Re_D=1e6 dP=10000 rho=1000 → C≈0.99188 Q≈0.008995

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) @ 2026-09-18T02:44:05.986Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T02:44:05.231Z
Last production check: 2026-09-18T02:44:05.231Z
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: long-radius-nozzle
Engine: long-radius-nozzle
REST: POST /api/v1/calc/long-radius-nozzle
MCP: execute_calculation with capability_id: "physics.fluid.long_radius_nozzle"
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

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.long_radius_nozzle"}}}'

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