Validation report

Orifice flow calculator: validation against ISO 5167-2

How we check that the orifice flow calculator applies ISO 5167-2 correctly: 11 reference cases covering liquids, gases and steam with corner, flange and D and D/2 tappings, the standard's limits of use, and steam density against IAPWS-IF97. Every input and result is published below so you can check them yourself.

What this check shows

It shows that the calculator evaluates ISO 5167-2 correctly: the Reader-Harris/Gallagher discharge coefficient, the expansibility factor, the iteration on Reynolds number, the permanent pressure loss, and the standard's limits of use.

Method

Each case was run through the calculator's server code, the same code that serves the calculator page. The results were compared with two references written independently of it:

1. fluids, an open-source Python library for fluid mechanics (version 1.3.1). Its orifice functions implement ISO 5167-2 and ASME MFC-3M.
2. A separate implementation written directly from the equations in ISO 5167-2:2003 §5.3.2, which the 2022 edition did not change.

The two references agree with each other to machine precision on every case. Mass flow is solved by iterating between the flow equation and the Reynolds-number-dependent C until C stops changing. Each reference uses the same density and viscosity as the calculator, so the comparison isolates the flow equations. Steam density is checked separately, below.

One detail: fluids adds two low-Reynolds-number terms from later work by Reader-Harris that are not in ISO 5167-2. Both are zero above Re_D ≈ 3 700. Every case here is above the ISO minimum of 5 000, so the comparison is against the ISO equation alone.

Equations checked

Results

“Calc” is the calculator; “Ref” is fluids 1.3.1, and the independent implementation gives the same values. Mass flow is in kg/s.

* Largest relative difference across C, ε, mass flow, Re_D and permanent pressure loss. Across all cases: C 2.5 × 10⁻¹⁰, mass flow 1.3 × 10⁻⁸.

Limits of use

ISO 5167-2 §5.3.1 sets the conditions under which the equations apply. Each limit was tested with an input just outside it. Every one produces a warning, and none of the 11 valid cases above produces a limit warning.

Steam density

For steam, the calculator works out density from pressure and temperature using IAPWS-IF97. At 45 superheated points from 1 to 160 bar a and 150 to 600 °C, it was compared with the iapws reference implementation. The largest difference is 4.1 × 10⁻¹⁶. The last column shows the error before the October 2026 correction described in the change log.

The isentropic exponent κ, which enters the expansibility factor, is also taken from IAPWS-IF97 for superheated steam as κ = ρw²/p, the definition used in ISO 5167. It matches the reference implementation to machine precision. Within 2 °C of saturation the calculator uses 1.135, the customary value for dry saturated steam.

Check it yourself

Case L2 (water, flange taps) with the same reference library. Enter the same values in the calculator and compare.

# pip install fluids==1.3.1
from fluids.flow_meter import differential_pressure_meter_solver, differential_pressure_meter_C_epsilon

# D = 100 mm, d = 50 mm, Δp = 25 kPa, water ρ = 998 kg/m³, μ = 1.0 mPa·s
# (k = 1e20 makes ε = 1, as for a liquid)
args = dict(D=0.100, D2=0.050, P1=200000, P2=175000, rho=998, mu=1.0e-3, k=1e20,
            meter_type='ISO 5167 orifice', taps='flange')
m = differential_pressure_meter_solver(**args)
C, eps = differential_pressure_meter_C_epsilon(m=m, **args)
print(f"m = {m:.6f} kg/s  C = {C:.6f}")   # m = 8.680648 kg/s  C = 0.605979

Change log

• 22 Oct 2026Isentropic exponent for steam now from IAPWS-IF97. κ was a fixed 1.135, the value for dry saturated steam. For superheated steam it is now calculated as κ = ρw²/p, which is about 1.24–1.32. Within 2 °C of saturation 1.135 is still used. κ affects only the expansibility factor: at 11 bar a and 200 °C, with β = 0.7 and Δp = 50 kPa, κ = 1.297 raises ε from 0.9813 to 0.9836, so the flow is 0.23 % higher.
• 22 Oct 2026Steam density corrected. Four IAPWS-IF97 Region 2 coefficients in the steam-density routine had the wrong power of ten. The error was negligible at low pressure but grew with pressure: +0.4 % at 11 bar a and 200 °C, +2.2 % at 40 bar a and 300 °C, and +8.7 % at 60 bar a and 300 °C. The largest error in the test grid was 20 %, at 160 bar a and 400 °C. Mass flow varies with √ρ, so superheated-steam flows were high by roughly half these figures. Liquid and gas results were not affected.
• 22 Oct 2026Limits of use aligned with ISO 5167-2:2022 §5.3.1. β now starts at 0.10 (was 0.20), the 12.5 mm minimum bore is checked, and the Reynolds-number limit depends on the tapping type and β. The previous fixed table was stricter than the standard and warned on some valid inputs. Calculated values did not change.
• 22 Oct 2026Formula reference corrected. The calculator page now shows the 2003/2022 expansibility equation, which the calculation was already using.

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