Gas Flow Two Paths: PT Correction vs Orifice Sizing

Gas flow pressure–temperature (PT) correction converts an existing actual volumetric flow rate to a specified set of base conditions. Orifice sizing determines the bore needed to produce a selected differential pressure at a target flow. The distinction is the unknown: base-condition flow for PT correction, or bore diameter for sizing. An orifice metering system can require both calculations—first determining mass flow from differential pressure, then expressing that flow as a base-condition volume rate.

Choose the Calculation by What You Need to Find

These are different uses of the gas-law and differential-pressure flow relationships described in Emerson’s Flow Measurement User Manual, March 2005, Sections 2.1 and 2.2. Its historical standard references should not be treated as the applicable edition for every installation.

There is no pressure-ratio threshold that changes PT correction into orifice sizing. Select the method by the required output, not by whether a pressure multiplier exceeds a particular number.

Path 1: Convert Actual Gas Flow to Base Conditions

For the same gas composition and conserved gas quantity, the real-gas relationship gives:

[
Q_b=Q_f
\left(\frac{P_f}{P_b}\right)
\left(\frac{T_b}{T_f}\right)
\left(\frac{Z_b}{Z_f}\right)
]

where:

• (Q_f): actual volumetric flow at flowing conditions, in m³/h.
• (Q_b): volumetric flow at the stated base conditions, in m³/h.
• (P_f), (P_b): flowing and base absolute pressures, in the same pressure unit.
• (T_f), (T_b): flowing and base absolute temperatures, in kelvin.
• (Z_f), (Z_b): dimensionless compressibility factors at the corresponding conditions.

The same ratios apply to a measured volume when the associated conditions are appropriately represented. Emerson gives this relationship in Section 2.1.6 of its flow manual.

Use absolute pressure, not gauge pressure:

[
P_{\mathrm{abs}}=P_{\mathrm{gauge}}+P_{\mathrm{atmospheric}}
]

Use the atmospheric pressure appropriate to the measurement or configured calculation basis. Convert Celsius to kelvin using (T_{\mathrm K}=t_{^\circ\mathrm C}+273.15). Specify the base pressure and temperature explicitly rather than relying on an unexplained “standard” or “normal” flow label.

Worked Example: Actual Flow to Base Flow

Assume the following illustrative inputs:

The base conditions and (Z) values are specified example inputs, not universal defaults or verified properties of a particular gas.

[
Q_b=
100.0
\left(\frac{600.0}{100.0}\right)
\left(\frac{288.15}{300.00}\right)
\left(\frac{1.0000}{0.9800}\right)
=588.0612\ldots\ \mathrm{m^3/h}
]

Rounded to four significant figures, the result is 588.1 m³/h at 100.0 kPa absolute and 288.15 K.

The larger volume rate does not mean more gas has been created. It expresses the same gas quantity per unit time at a lower reference density. Reversing all three ratios returns the original 100.0 m³/h. When flowing and base conditions—including (Z)—are identical, the conversion factor is 1.

Choose Compressibility Data by Gas and Conditions

(Z) accounts for departures from ideal-gas behavior and varies with gas composition, pressure, and temperature. It is not the same as the orifice gas expansion factor. Emerson’s Rosemount DP Flow Terminology, Part 1 distinguishes these terms.

A rule such as “(f_p) above 10 needs AGA8” is not a sufficient selection criterion: it does not define (f_p), establish the gas composition, or identify the property model’s applicable range. Use the property method and edition required by the project, contract, or configured flow computer, and check its composition, pressure, and temperature limits. Emerson discusses AGA Report No. 8 as a source of compressibility values for natural-gas mixtures; this does not make it a universal model for every industrial gas.

Path 2: Size an Orifice Bore for a Target Flow

For an orifice meter, a consistent SI form of the mass-flow equation is:

[
\dot m=
C_d\varepsilon E
\frac{\pi d^2}{4}
\sqrt{2\rho_1\Delta p}
]

with:

[
\beta=\frac{d}{D},
\qquad
E=\frac{1}{\sqrt{1-\beta^4}}
]

where:

• (\dot m): mass flow, kg/s.
• (C_d): dimensionless discharge coefficient.
• (\varepsilon): dimensionless gas expansibility factor, also written (Y) or (Y_1).
• (E): dimensionless velocity-of-approach factor.
• (d): orifice bore diameter at operating temperature, m.
• (D): pipe internal diameter at operating temperature, m.
• (\rho_1): upstream gas density, kg/m³.
• (\Delta p): differential pressure between the specified pressure taps, Pa.
• (\beta): dimensionless bore-to-pipe diameter ratio.

Emerson presents the mass-flow relationship and defines these factors in its flow manual and Rosemount terminology note. (E) accounts for the diameter-ratio relationship; (\varepsilon) accounts for gas density change through the primary element. Neither replaces the real-gas factor (Z).

For sizing, the target flow and differential pressure are known, while (d) is unknown. Because changing (d) changes (\beta), and the discharge and expansibility coefficients depend on the applicable flow and geometry relationships, practical sizing generally requires iteration. A fixed (C_d) is not a universal plate-sizing rule.

Worked Example: Bore Calculation with Fixed Illustrative Coefficients

To isolate the bore calculation, assume:

The coefficients are assumed for this arithmetic example. They have not been established for a particular plate, tapping arrangement, gas, or Reynolds number.

For fixed coefficients, define:

[
K=
\frac{\dot m}
{C_d\varepsilon(\pi/4)\sqrt{2\rho_1\Delta p}}
]

Here (K) has units of m². Rearranging the flow equation gives:

[
d=
\left(
\frac{K^2}{1+K^2/D^4}
\right)^{1/4}
]

Substitution gives a bore of 50.00 mm, rounded to four significant figures. Therefore:

[
\beta=\frac{50.00}{100.0}=0.5000
]

[
E=\frac{1}{\sqrt{1-0.5000^4}}=1.032796\ldots
]

Substituting the bore back into the original equation gives:

[
\dot m=
0.6100(0.9800)(1.032796)
\frac{\pi(0.05000)^2}{4}
\sqrt{2(5.000)(10{,}000)}
]

[
\dot m\approx0.3834\ \mathrm{kg/s}
]

This is a bore result under the stated fixed-coefficient assumptions, not a plate specification ready for manufacture. A real sizing calculation must establish the applicable coefficients, gas properties, installation conditions, and operating range.

Beta Alone Does Not Establish Acceptability

A calculated beta ratio is a geometry check, not a complete acceptance test. The applicable method also constrains plate geometry, tapping arrangement, pipe size, Reynolds number, and installation conditions.

The official ISO 5167-2:2022 overview identifies flange, corner, and (D) and (D/2) pressure tappings. Its stated applicability is single-phase flow that remains subsonic throughout the measuring section; pulsating flow is excluded. It also excludes pipe diameters below 50 mm or above 1,000 mm, and pipe Reynolds numbers below 5,000. These overview limits are not a substitute for the full, configuration-specific requirements of ISO 5167-1 and ISO 5167-2.

For an actual sizing job, record the governing standard and edition, tapping arrangement, operating-temperature dimensions, density and viscosity basis, expansibility method, and minimum-to-maximum operating conditions.

How the Two Paths Work Together

An orifice system can calculate mass flow from differential pressure and then convert that result to either actual or base-condition volumetric flow:

[
Q_f=\frac{\dot m}{\rho_1},
\qquad
Q_b=\frac{\dot m}{\rho_b}
]

where (Q_f) and (Q_b) are in m³/s when mass flow is in kg/s and density is in kg/m³. Multiply by 3,600 for m³/h. (\rho_b) is the gas density at the declared base conditions. Emerson describes this conversion from orifice mass flow to base-condition volume flow in Section 2.2.3 of its manual.

This explains why “metering proves volume; sizing proves the plate” is misleading. Metering estimates flow from measurements and a model. Sizing selects geometry for specified conditions. Neither calculation alone establishes field measurement accuracy or installation compliance.

Wrong Choices and Their Consequences

Using Gauge Pressure in the PT Ratio

In the PT example, suppose 600 kPa absolute corresponds to 500 kPa gauge plus an assumed local atmospheric pressure of 100 kPa.

Using 500 instead of 600 in the pressure ratio would give:

[
Q_{b,\mathrm{wrong}}=
100.0
\left(\frac{500.0}{100.0}\right)
\left(\frac{288.15}{300.00}\right)
\left(\frac{1.0000}{0.9800}\right)
\approx490.1\ \mathrm{m^3/h}
]

That is 16.7% below the correctly calculated result, using the correct result as the percentage-error denominator.

Treating Differential Pressure as Actual Volumetric Flow

A differential-pressure reading is not (Q_f). It must first enter the applicable orifice flow equation. With geometry, density, and coefficients held constant, flow varies with the square root of differential pressure: 25% of the reference differential pressure corresponds to 50% of the reference flow. This follows directly from the orifice equation.

Before processing a transmitter or PLC value, establish whether it represents raw differential pressure, square-root-extracted flow, or already compensated flow. Applying another square root or another base-condition conversion changes the meaning of the signal and can duplicate processing already performed.

Treating the Velocity-of-Approach Factor as Optional

For the example’s (\beta=0.5000), (E=1.032796). Setting (E=1) while keeping all other example inputs unchanged would make the calculated mass flow approximately 3.18% lower, relative to the result with (E) included.

This percentage belongs to this beta ratio and these fixed assumptions; it is not a general orifice-meter error allowance.

Checklist Before Using the Result

• Identify the unknown: base-condition flow, mass flow, bore diameter, or beta ratio.
• Confirm what the incoming signal represents and which corrections have already been applied.
• For PT correction, record both pressure and temperature bases and the source of each (Z) value.
• For orifice sizing, use pipe internal diameter—not nominal pipe size—and dimensions appropriate to operating temperature.
• Establish (C_d) and expansibility from the selected method and configuration rather than copying illustrative values.
• Check the applicable geometry, Reynolds-number, pressure-ratio, and installation limits across the intended operating range.
• Reject nonpositive absolute pressures, absolute temperatures, densities, or (Z) values. For the forward-flow orifice equation shown, require (0<d<D) and nonnegative differential pressure; reverse flow needs an appropriate configuration and method.
• Retain unrounded intermediate values and round the final result to precision justified by the inputs.

A reproducible calculation provides a reference for engineering review. Field acceptance still depends on the installed equipment, configuration, measurement uncertainty, and required inspection or calibration procedure—not arithmetic agreement alone.