Verified calculation capability

Hagen–Poiseuille Calculation Capability

Laminar circular-pipe Q=πΔpD⁴/(128μL). Not Darcy f, not Colebrook, not Q=Av, not Manning. · Physics · Fluid

Capability ID physics.fluid.poiseuille · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Discharge

Discharge: Q = π Δp D⁴ / (128 μ L)
Pressure drop: Δp = 128 μ L Q / (π D⁴)
Mean speed: v = 4Q / (π D²)

Solve modes: flow · pressure · diameter · viscosity

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`dP`	Pressure drop in Pa. Required except pressure invert. Alternatives: deltaP, dP_Pa, dp.	—	input / output
`Q`	Discharge in m³/s. Required for invert. Alternatives: flow, Q_m3_s. Do not send with flow mode.	—	input / output
`D`	Inner diameter in m. Required except diameter invert. Alternatives: D_m, diameter.	—	input / output
`L`	Pipe length in m. Alternative: L_m.	—	input / output
`mu`	Dynamic viscosity in Pa·s. Required except viscosity invert. Alternatives: mu_Pa_s, viscosity.	—	input / output
`v`	velocity	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Laminar Hagen–Poiseuille: Q = π Δp D⁴ / (128 μ L); circular, fully developed, Newtonian
Mean speed v = 4Q/(π D²) is reported, not an input
Not Darcy f, not Colebrook, not Q=Av, not Manning

Not supported

Darcy f
Colebrook ε/Re
Q=Av
Manning n

Example

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

dP=1000 D=0.002 L=1 mu=0.001 → Q=π×1.25e-7

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) @ 2026-09-17T09:03:11.906Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T09:03:11.074Z
Last production check: 2026-09-17T09:03:11.074Z
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: hagen-poiseuille
Engine: hagen-poiseuille
REST: POST /api/v1/calc/hagen-poiseuille
MCP: execute_calculation with capability_id: "physics.fluid.poiseuille"
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 — Dynamic viscosity
White, F.M. Fluid Mechanics — Hagen–Poiseuille flow

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.poiseuille"}}}'

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