Orifice plate calculator to ISO 5167-2

Size the bore of a new orifice plate, or check the flow or differential pressure of an existing one. Corner, flange, and D and D/2 tappings, for gas, liquid, steam and water, with the Reader-Harris/Gallagher equation from ISO 5167-2:2003.

Try it free Opens a sample orifice plate. No account needed.

Solve for flow, bore or ΔP

Unknown	You enter	Typical use
Flow rate	Bore d and differential pressure ΔP	Checking an installed plate, or setting up a transmitter range
Bore d	Flow rate and ΔP	Sizing a new plate for a chosen ΔP range
Differential pressure ΔP	Bore d and flow rate	Checking that a plate fits a transmitter range

Plus the fluid (density and viscosity, or computed from IAPWS-IF97 for water and steam), the pressure and temperature, and the isentropic exponent κ for gas and steam. Every field takes its own unit, so you can type a datasheet in as it is written.

Tappings

The three standard tapping arrangements share one equation for the discharge coefficient and differ only in where the pressure is measured, which sets L₁ and L′₂.

Corner tappings	At the faces of the plate	L₁ = L′₂ = 0
Flange tappings	25.4 mm (1 in) from each face	L₁ = L′₂ = 25.4 / D
D and D/2 tappings	D upstream and D/2 downstream	L₁ = 1, L′₂ = 0.47

FlowCalc also covers the quadrant-edge orifice plate from ISO/TR 15377, for low Reynolds numbers.

The equations

Mass flow through the plate:

qm = C / √(1 − β⁴) · ε · (π/4) d² · √(2 ΔP ρ₁)

Discharge coefficient C, the Reader-Harris/Gallagher equation:

C = 0.5961 + 0.0261 β² − 0.216 β⁸ + 0.000521 (10⁶ β / Re_D)^0.7
  + (0.0188 + 0.0063 A) β^3.5 (10⁶ / Re_D)^0.3
  + (0.043 + 0.080 e^(−10 L₁) − 0.123 e^(−7 L₁)) (1 − 0.11 A) β⁴ / (1 − β⁴)
  − 0.031 (M′₂ − 0.8 M′₂^1.1) β^1.3

A = (19 000 β / Re_D)^0.8        M′₂ = 2 L′₂ / (1 − β)

When D < 71.12 mm, add 0.011 (0.75 − β) (2.8 − D / 25.4), D in mm.

Expansion factor ε for gas and steam (1 for liquids):

ε = 1 − (0.351 + 0.256 β⁴ + 0.93 β⁸) [1 − (p₂ / p₁)^(1/κ)]

C depends on Re_D, and Re_D depends on the flow, so the flow is found by iteration. FlowCalc does this for all three unknowns.

Validity limits

ISO 5167-2 only gives C within these limits. FlowCalc checks every one and marks any value outside them, so you see the result and know it is outside the standard.

Bore d	d ≥ 12.5 mm
Pipe diameter D	50 mm ≤ D ≤ 1000 mm
Diameter ratio β	0.1 ≤ β ≤ 0.75
Reynolds number, corner and D and D/2	Re_D ≥ 5000 for β ≤ 0.56, Re_D ≥ 16 000 β² for β > 0.56
Reynolds number, flange	Re_D ≥ 5000 and Re_D ≥ 170 β² D (D in mm)
Expansion factor ε	p₂/p₁ ≥ 0.75

Uncertainty

The uncertainty of C from ISO 5167-2, shown with every result:

0.1 ≤ β < 0.2	(0.7 − β) %
0.2 ≤ β ≤ 0.6	0.5 %
0.6 < β ≤ 0.75	(1.667 β − 0.5) %

Added on top: 0.9 (0.75 − β)(2.8 − D/25.4) % when D is below 71.12 mm, and 0.5 % when β is above 0.5 and Re_D is below 10 000.

Worked example

The sample plate that opens when you try FlowCalc, solved for flow:

Inputs

Fluid: Water, 20 °C, 1.01325 bar(a)
Density, viscosity: 1000 kg/m³, 1 cP
Pipe D, bore d: 100 mm, 60 mm (β = 0.6)
Tappings: Corner
Differential pressure: 10 kPa (100 mbar)

Result

Mass flow: 29 771 kg/h (65 634 lb/h)
Re_D: 105 293
C: 0.6102
ε: 1 (liquid)
Uncertainty of C: 0.50 %
Permanent pressure loss ΔW: 6.27 kPa

Open this example and change it

Also checked

Plate thickness: The plate thickness limits for your pipe size, shown on the report.
Drain and vent holes: The flow correction and added uncertainty for a drain or vent hole in the plate, from ISO/TR 15377.
Thermal expansion: Bore and pipe diameter corrected to the operating temperature, from the plate and pipe materials.
Choked flow and cavitation: Gas and steam are checked for critical flow, water for cavitation.
Permanent pressure loss: ΔW, the pressure the plate costs you downstream, from the ISO 5167-2 formula.
Straight lengths: Upstream and downstream lengths for 12 fittings at your β, on the report.

The straight-length tables for orifice plates, nozzles and Venturi tubes are on the straight lengths page.

Keep your plates, print the datasheet

The trial is free and needs no account. With an account, every plate is saved, shared with your team, and prints as a PDF datasheet with the limits, uncertainty and straight lengths.

Try it free Sample report (PDF)