Orifice Flow Meter Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified with errata that must be applied at binding time.

Area

Thermodynamics, Fluids & Aero

Tranche

tranche-4

Evidence ID

t4-273

Ledger rows

1

No ledger note is attached.

Review findings

The flow-rate equation itself is conditionally correct, but the specification needs review before release. Define whether velocity means pipe velocity or orifice-bore velocity, restrict the instrument to incompressible flow or add compressibility treatment, define A2 explicitly, and state ISO 5167 geometry, tap, and applicability constraints. The honest-label statement about approximate Cd is appropriate but insufficient without these operating restrictions.

Formula and scope findings

• The stated flow formula is standard for steady, incompressible flow through a thin-plate orifice when A2 is the orifice-bore area, A2=πd²/4, and β=d/D.
• The formula does not define the reported velocity. Velocity could mean pipe velocity, V1=Q/A1, or orifice-bore velocity, V2=Q/A2; these are different outputs.
• For gases or other compressible fluids, the formula is incomplete because an expansibility factor is generally required; the claim must be limited to incompressible or sufficiently low-Mach-number flow unless compressibility is added.
• Cd is not a universal constant or merely a generic table lookup; it depends on Reynolds number, β, tap configuration, edge geometry, and installation details. ISO 5167 applicability limits must be enforced.
• The differential pressure must correspond to the specified pressure-tap arrangement and reference conditions; this is not stated.

Unit assumptions

• All test vectors use SI units: diameters in m, differential pressure in Pa, density in kg/m³, and flow rate in m³/s.
• d and D must use the same length units because β=d/D is dimensionless.
• A2=πd²/4 and A1=πD²/4.
• The stated formula assumes incompressible flow with density representative of the flowing fluid at the measurement conditions.
• Pipe velocity is defined here as V1=Q/A1; orifice-bore velocity is defined as V2=Q/A2.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes undefined behavior at d=D because 1−β⁴ becomes zero, and at negative ΔP because the square-root argument becomes negative. It also does not specify whether velocity is pipe velocity or orifice velocity, nor how pressure direction should be represented.

Errata and corrections

Tranche errata

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "D_m": 0.1,
    "d_m": 0.05,
    "delta_P_Pa": 10000,
    "Cd": 0.61,
    "rho_kg_m3": 1000
  },
  "expected_outputs": {
    "Q_m3_s": 0.005532088,
    "velocity_pipe_m_s": 0.704367,
    "velocity_orifice_m_s": 2.817469
  },
  "working": "β=d/D=0.05/0.1=0.5; β⁴=0.5⁴=0.0625. A2=π(0.05²)/4=0.001963495 m². √[2ΔP/(ρ(1−β⁴))]=√[20000/(1000×0.9375)]=√21.333333=4.618802 m/s. Q=0.61×0.001963495×4.618802=0.005532088 m³/s. A1=π(0.1²)/4=0.007853982 m². V1=Q/A1=0.005532088/0.007853982=0.704367 m/s. V2=Q/A2=0.005532088/0.001963495=2.817469 m/s."
}

Related workflows

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json