Orifice Sizing
Reynolds Number (ReD):-
Beta Ratio (β):-
Expansion Factor (ε₁):-
Discharge Coeff. (C):-
Calculated Orifice Diameter (d):-
Overall Pressure Loss (Δω):-
Sonic Velocity (for gases):-
Range of Validity Checks
Pressure Ratio (τ ≥ 0.75):-
Orifice Diameter (d ≥ 12.5mm):-
Pipe Diameter (50-1000mm):-
Beta Ratio (0.2 ≤ β ≤ 0.75):-
Reynolds Number Limit:-
Flow is Subsonic:-
Technical Notes
Variable Definitions
-
D: pipe internal diameter (m) (computed from DN
and schedule).
- d: orifice bore diameter (m) (calculated).
-
β: beta ratio = d/D.
- ṁ: mass flow rate (kg/s).
-
ρ: upstream density (kg/m³), μ:
dynamic viscosity (Pa·s).
-
P₁: upstream absolute pressure (Pa),
ΔP: differential pressure (Pa).
-
C: discharge coefficient (–) from ISO 5167-type
correlation.
-
ε₁: expansibility (expansion) factor for gases
(–).
-
ReD: Reynolds number based on pipe diameter.
Formulas / Logic
-
Reynolds number:
ReD = 4ṁ / (π μ D).
-
Flow equation (orifice): rearranged to solve for
d iteratively:
ṁ = C ε₁ (π d²/4) √(2 ρ ΔP) / √(1−β⁴).
-
Discharge coefficient: ISO 5167-style correlation
using β,
ReD, and tap locations (L1, L2).
-
Gas expansibility: screening form:
ε₁ = 1 − (0.41 + 0.35β⁴)·(ΔP/(k·P₁))
(bounded to ≥ 0).
-
Permanent pressure loss: estimated as a function
of C, β, and
ΔP (screening).
-
Sonic check (gas):
a = √(k·P₁/ρ), compare with orifice
velocity to flag subsonic flow.
This is a sizing / screening calculator. Final design should
consider plate thickness, edge sharpness, vena contracta, tap
details, installation straight lengths, and meter uncertainty per
the standard.
Assumptions / Notes
-
Inputs are assumed at upstream flowing conditions. For gases,
ensure absolute pressure and consistent density.
-
Validity limits shown are conservative checks. ISO 5167 validity
depends on β, D, tapping, and Re and should be confirmed for the
final selected geometry.
-
Multiphase flow, non-Newtonian fluids, pulsating flow, and
significant compressibility effects beyond the expansibility
factor are outside this tool’s scope.
Standards / References
-
ISO 5167 — Measurement of fluid flow by means of
pressure differential devices inserted in circular cross-section
conduits running full.
-
AS 2360.1.1 (where applicable) — orifice plate /
differential pressure device practice.
-
Common engineering references: ISO 5167 supporting correlations
(Reader-Harris/Gallagher), and DP metering handbooks.