Source: https://guthlabs.ai/docs/instruments/orifice-flow-meter-calculator/
instrument / verified-with-binding-errata
# Orifice Flow Meter Calculator
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## 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
**velocity_orifice_m_s** · vector 2
2.025912
2.024911
minor: inconsistent with her own correct Q/Ao in 4th digit
## 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
[Pipe & Pump Benchmeter 1]()
## 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`