Verified calculation capability

Elbow flow meter Calculation Capability

90° elbow tap meter Q=C A √(2Δp/ρ) with C=√((R/D)/2). Not pipe-bend K, not Pitot C=1, not venturi, not ISO 5167-6 wedge, not Q=Av, not Darcy. · Physics · Fluid

Capability ID physics.fluid.elbow_meter · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Discharge

Discharge: Q = C A √(2Δp / ρ)
Elbow C: C = √((R/D) / 2)
Area: A = (π/4) D²

Solve modes: flow · pressure · coefficient

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`D`	Pipe inside diameter in m. Required. Envelope [25 mm, 600 mm]. Alternatives: D_m, pipe, pipe_D. Do not send nozzle D1+D2 or orifice d+D.	—	input / output
`R`	Bend centerline radius in m. Required unless rd. Alternatives: R_m, R_c, Rc, R_centerline, bend_radius. Not Chezy hydraulic radius.	—	input / output
`rd`	Centerline R/D. Alternative to R. Envelope [1.0, 3.0]. Alternatives: R_over_D, RD, r_over_d, R_D.	—	input / output
`dP`	Inner-to-outer tap 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
`A`	—	—	output
`C`	—	—	output
`Cd`	—	—	output
`v`	velocity	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

90° elbow tap meter: Q = C A √(2Δp/ρ); C=√((R/D)/2); A=(π/4)D²; inner/outer radius taps; incompressible; C is reported, not an input
R/D∈[1.0, 3.0]; D∈[25 mm, 600 mm]; 90° only; C from R/D, not a given Pitot C=1
Not pipe-bend K=0.21 (θ/90)/√(R/D), not Pitot v=C√(2Δp/ρ), not venturi, not ISO 5167-6 wedge, not Q=Av, not Darcy f

Not supported

pipe-bend K
Pitot C=1
venturi
ISO 5167-6 wedge
given C_d
Q=Av
Darcy f
variable θ

Example

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

D=0.1 R=0.15 dP=10000 rho=1000 → C≈0.86603 Q≈0.030418

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) @ 2026-09-18T10:48:34.503Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T10:48:33.674Z
Last production check: 2026-09-18T10:48:33.674Z
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: elbow-meter
Engine: elbow-meter
REST: POST /api/v1/calc/elbow-meter
MCP: execute_calculation with capability_id: "physics.fluid.elbow_meter"
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
Elbow tap meter — centrifugal Δp — C=√((R/D)/2) from inner/outer taps

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.elbow_meter"}}}'

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