Verified calculation capability

Orifice discharge Calculation Capability

Sharp-edged orifice. Tank Q=C_d A √(2gH). Meter Q=C_d E A_t √(2Δp/ρ) with E=1/√(1−β⁴). Not a weir, not Q=Av, not Darcy, not Manning, not compressible ISO ε. · Physics · Fluid

Capability ID physics.fluid.orifice · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Tank

Tank: Q = C_d A √(2g H)
Meter: Q = C_d E A_t √(2Δp/ρ)
Approach: E = 1 / √(1 − β⁴)

Solve modes: tank · meter

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`d`	Orifice diameter in m. Tank may use A instead of d. Meter requires d and D.	—	input / output
`D`	Pipe inner diameter in m. Meter only. d must be smaller than D.	—	input / output
`A`	Orifice area in m². Tank alternative to d. Do not send both.	—	input / output
`H`	Tank head on the orifice in m. Give H or Q, not both. Not used on meter.	—	input / output
`dP`	Meter differential pressure in Pa. Give Δp or Q, not both.	—	input / output
`Q`	Discharge in m³/s. Inverts H (tank) or Δp (meter).	—	input / output
`rho`	Density in kg/m³. Required for meter.	—	input / output
`Cd`	Discharge coefficient. Default 0.61. Must be in (0, 1].	—	input / output
`g`	Gravity in m/s². Default 9.80665. Tank only.	—	input / output
`beta`	—	—	output
`E`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Sharp-edged orifice; SI; default C_d=0.61; C_d in (0, 1]
Tank: Q=C_d A √(2gH); not a weir H^{3/2}
Meter: Q=C_d E A_t √(2Δp/ρ), E=1/√(1−β⁴); incompressible; user C_d
Not weir, not Q=Av, not Darcy, not Manning, not compressible ISO ε(Re)

Not supported

weir overflow
Q=Av identities
Darcy–Weisbach
Manning
compressible ISO ε(Re)
Reader–Harris/Gallagher C(Re)
pump curves

Example

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

d=0.05 H=2 → Q=0.61 (πd²/4) √(2gH)

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: 15/15 calculation tests · golden 1/1 · boundary 9/9 · 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) @ 2026-09-17T03:09:03.307Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T03:09:02.494Z
Last production check: 2026-09-17T03:09:02.494Z
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: orifice-discharge
Engine: orifice-discharge
REST: POST /api/v1/calc/orifice-discharge
MCP: execute_calculation with capability_id: "physics.fluid.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

ISO 5167-2 — Measurement of fluid flow by means of pressure differential devices — Orifice plates — Incompressible discharge with velocity-of-approach factor
Munson, B.R., Young, D.F., and Okiishi, T.H. Fundamentals of Fluid Mechanics — Orifice discharge; Torricelli

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.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.