Verified calculation capability

ISO 5167 orifice plate Calculation Capability

ISO 5167-2 orifice plate Q=C E A2 √(2Δp/ρ) with Reader–Harris/Gallagher C from β, Re_D, and tapping. Not tank orifice C_d A √(2gH), not given C_d=0.61, not ISA 1932, not venturi C_d=0.98, not Q=Av, not Darcy. · Physics · Fluid

Capability ID physics.fluid.iso_orifice · 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 = d/D · E = 1/√(1 − β⁴)
RHG C (corner L1=L2′=0): C = 0.5961 + 0.0261 β² − 0.216 β⁸ + 0.000521 (10⁶ β / Re_D)^0.7 + (0.0188 + 0.0063 A) β^3.5 (10⁶ / Re_D)^0.3

Solve modes: flow · pressure · coefficient

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`D`	Pipe diameter in m. Required. D in [0.05, 1.0]. Alternative: D_m, pipe_D. Do not send D1+D2.	—	input / output
`d`	Bore diameter in m. Required unless beta. d ≥ 0.0125 m. Alternatives: d_m, bore, D_bore. Do not mix with beta.	—	input / output
`beta`	d/D in [0.10, 0.75]. Alternative to d. Alternative: diameter_ratio.	—	input / output
`Re_D`	Pipe Reynolds number on D. Required. ≥5000 (β≤0.56) or 16000 β² (β>0.56). Alternatives: Re, ReD. Do not send ρ, μ, v.	—	input / output
`tapping`	corner (default) or flange. D-D/2 is out of scope. Alternatives: taps, tap.	—	input / output
`dP`	Upstream-to-vena 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 5167-2 orifice plate: Q = C E A2 √(2Δp/ρ); Reader–Harris/Gallagher C from β, Re_D, and tapping; incompressible ε=1; C is reported, not an input
Corner tappings default (L1=L2′=0); flange L1=L2′=25.4 mm/D; β∈[0.10,0.75]; D∈[50 mm,1000 mm]; d≥12.5 mm; Re_D≥5000 (β≤0.56) or 16000 β² (β>0.56)
Not tank orifice C_d A √(2gH), not given C_d=0.61, not ISA 1932 nozzle, not venturi C_d=0.98, not Q=Av, not Darcy f, not D-D/2 tappings, not compressible ε

Not supported

tank C_d A √(2gH)
given C_d=0.61
ISA 1932 nozzle
venturi C_d=0.98
Q=Av
Darcy f
compressible ε
D-D/2 tappings

Example

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

D=0.1 d=0.05 Re_D=1e6 dP=10000 rho=1000 corner → C≈0.60378 Q≈0.005476

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 STALE (1 capability; 163 remain CURRENT) @ 2026-09-17T23:16:16.380Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T23:04:34.157Z
Last production check: 2026-09-17T23:04:34.157Z
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: iso-orifice
Engine: iso-orifice
REST: POST /api/v1/calc/iso-orifice
MCP: execute_calculation with capability_id: "physics.fluid.iso_orifice"
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.iso_orifice"}}}'

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