Sizing Variable Area Flowmeters for Gases: Correctly Converting Standard Conditions, Operating Pressure and Gas Temperature

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A variable area flowmeter can indicate an apparently clear value in a gas line and still deviate significantly from the actually expected flow rate. The cause is often not a defective measuring instrument, but rather that the flowmeter was sized for different pressure or temperature conditions than those actually encountered later in the process.

This relationship is particularly important for gases because their density depends strongly on pressure and temperature. A float reacts directly to the density of the flowing medium. If the process conditions change, the relationship between float position and flow rate therefore changes as well.

A scale indication such as:

0 … 10 m³/h

is therefore only fully meaningful for a gas if it is also known for which:

• gas,
• pressure level,
• temperature level,
• reference or standard condition

the scale was designed.

For the correct sizing of a variable area flowmeter for gases, gas type, operating pressure, gas temperature and the desired flow unit must therefore always be considered together.

A suitable industrial instrument is the Siemens SITRANS FVA250 variable area flowmeter offered by ICS Schneider. The instrument is suitable for liquids, gases and steam and, depending on the version, can be configured for demanding process conditions with high pressures and temperatures.

Additional solutions can be found under Flow Measurement Technology and specifically under Variable Area Flowmeters at ICS Schneider.

How does a variable area flowmeter work?

A variable area flowmeter operates according to the principle of a variable flow cross-section. The medium flows through a measuring section whose free flow area changes with the position of the float.

The flowing medium lifts the float until an equilibrium is established between the acting forces.

In simplified terms, these include:

• the weight of the float,
• buoyancy,
• flow force.

As the flow rate increases, the float moves further upward or into a region with a larger free flow cross-section.

Its position then corresponds to a specific flow rate.

With the SITRANS FVA250

the movement of the float is transmitted to the external indicator via a magnetic system.

This enables direct local flow indication even with an all-metal design.

Why are gases particularly critical when sizing the instrument?

With a liquid, density usually changes only comparatively little as a result of moderate pressure variations.

With a gas, this is different.

Gas density depends substantially on:

• absolute pressure,
• absolute temperature,
• gas type

.

If the pressure increases

the gas becomes denser.

If the temperature increases

the gas becomes less dense at the same pressure.

For the float, this means

that the same float position under changed process conditions does not necessarily correspond to the same actual volumetric flow rate.

For gases, the following question must therefore always be asked

For which gas density was this scale designed?

Distinguishing operating volume and standard volume

With gas flow rates, at least two different quantities must be distinguished.

Operating volumetric flow

The operating volumetric flow describes the actual volume occupied by the gas under the current process conditions.

A typical unit is:

m³/h operating conditions

Standard volumetric flow

With standard volumetric flow, the same quantity of gas is converted back to defined reference conditions.

A typical unit is:

Nm³/h

This means

one cubic metre of gas at high pressure contains considerably more gas mass or amount of substance than one cubic metre of the same gas at atmospheric pressure.

Therefore, for example

1 m³/h operating volume

and:

1 Nm³/h

can describe completely different gas flow rates in the same system.

What does Nm³/h mean?

The “N” in Nm³/h indicates that the gas volumetric flow has been referenced to defined standard conditions.

Typical reference conditions are, for example

TN = 0 °C = 273,15 K

and:

pN = 1,01325 bar abs

However, caution is required

The specific reference condition must always be stated or checked.

In different technical applications, for example:

• 15 °C,
• 20 °C,
• other reference pressures

may also be used.

Therefore, a value such as

100 Nm³/h

is technically only fully defined when the underlying reference condition is also known.

Why are the scale reference conditions decisive?

A direct flow scale of a variable area flowmeter is designed for specific medium and operating-condition data.

For the SITRANS FVA250, Siemens specifies the following reference data for gas measuring ranges

• gas density: 1,293 kg/m³,
• temperature: 0 °C,
• viscosity: 0,0181 mPa·s,
• gauge pressure: pe = 0 bar.

These values clearly demonstrate

that a specified gas measuring range must not be considered independently of:

density + pressure + temperature + gas type

.

For a specific application

the instrument can therefore be configured with a product scale matched to the application.

This is generally preferable

if the operating conditions are already known when the instrument is ordered.

A correctly configured scale significantly reduces subsequent conversion errors.

Why must absolute pressure always be used?

One of the most common errors in gas conversions is using gauge pressure instead of absolute pressure.

For example, a pressure gauge indicates

5 bar

.

This normally means

5 bar gauge pressure

For gas-state calculations, however, the following is required

pabs

As an approximation

pabs = pe + patm

At an atmospheric pressure of approximately 1,013 bar, this gives

5 bar(g) ≈ 6,013 bar(a)

A calculation using only 5 bar

would therefore result in a systematic error.

Basic rule

Gas conversions are performed using absolute pressure.

Why must gas temperature be entered in Kelvin?

Temperature must also not simply be entered in degrees Celsius in a gas equation.

Absolute temperature is used

in Kelvin:

T [K] = t [°C] + 273,15

Example

20 °C = 293,15 K

and

50 °C = 323,15 K

Why is this important?

A calculation using:

20 / 0

for 20 °C compared with 0 °C would not be physically meaningful.

Using Kelvin, by contrast, allows the ratio of absolute temperatures to be represented correctly.

How pressure and temperature change gas density

For an approximately ideal gas:

ρ ∝ p / T

Gas density therefore increases

when:

• absolute pressure increases,
• temperature decreases.

Gas density decreases

when:

• absolute pressure decreases,
• temperature increases.

This relationship directly influences

the forces acting on the float.

For the same gas

the density can be approximately compared using:

ρ2 / ρ1 ≈ (p2 / p1) × (T1 / T2)

.

At high pressures

real gas behavior can increasingly deviate from the ideal gas equation.

In this case, the:

compressibility factor Z

may also need to be taken into account.

Do not confuse two different conversions

With variable area flowmeters, two different calculations are often confused with one another.

1. State conversion of a gas volume

Here, an already known actual volumetric flow is converted from one pressure and temperature level to another.

The gas equation forms the basis for this calculation.

2. Correction of a variable area flowmeter scale

Here, it must be taken into account that the gas density itself influences the position of the float.

For this reason, the approximate correction involves:

a square-root relationship

.

This means

The simple standard-volume equation must not be used directly as a correction formula for an unchanged variable area flowmeter scale.

Correcting a variable area flowmeter scale for changed pressure and temperature

If the same gas is used and an existing variable area flowmeter scale is referenced to different pressure and temperature conditions, an approximate correction can be made.

For an indication scaled to standard or reference volume, the following may approximately apply

Qcorr ≈ Qindication × √[(pB,abs / pRef,abs) × (TRef / TB)]

Where

• Qindication = indicated flow rate,
• pB,abs = actual absolute pressure at the measuring instrument,
• pRef,abs = reference absolute pressure of the scale,
• TB = actual gas temperature in Kelvin,
• TRef = reference temperature in Kelvin.

Important

This relationship is a technical approximation.

For exact sizing, the following may additionally be relevant:

• gas type,
• float density,
• viscosity,
• Reynolds number,
• compressibility factor,
• specific measuring tube and float geometry.

For new sizing

a factory scale designed for the actual process conditions is therefore preferable to a subsequent approximate correction.

Converting operating volume to standard volume

If the actual operating volumetric flow is already known, the pure state conversion is performed differently.

For an idealized gas, the following approximately applies

QN = QB × (pB,abs / pN,abs) × (TN / TB)

For real gas behavior, the following can additionally apply

QN = QB × (pB,abs / pN,abs) × (TN / TB) × (ZN / ZB)

This equation answers the question

What volume would the same quantity of gas occupy under standard conditions?

It does not directly answer the question

How must an incorrectly scaled variable area flowmeter indication be corrected?

What happens when using a different gas?

A variable area flowmeter scale depends not only on pressure and temperature, but also on the gas being used.

The main reason

is the different gas density.

Examples

The densities of:

• hydrogen,
• helium,
• nitrogen,
• air,
• argon,
• carbon dioxide

differ significantly.

A scale designed for air

therefore cannot be used without verification for:

CO₂

or:

hydrogen

.

As an approximate estimate

a density correction using a square-root relationship can be used under comparable operating conditions.

For reliable instrument sizing

however, the actual gas should already be specified during the sizing process.

Practical example of pressure and temperature correction

An existing variable area flowmeter has a gas scale referenced to approximately 0 °C and atmospheric pressure. The same gas is later to be used at an elevated operating pressure.

Reference conditions

pRef,abs = 1,013 bar

TRef = 273,15 K

Actual operating conditions

Gauge pressure:

pe = 2,0 bar

The absolute pressure is therefore approximately

pB,abs = 3,013 bar

Gas temperature

20 °C = 293,15 K

Indicated scale value

Qindication = 6,0 m³/h

Approximate correction factor

K ≈ √[(3,013 / 1,013) × (273,15 / 293,15)]

This gives approximately

K ≈ 1,67

The corrected referenced flow rate is therefore approximately

Qcorr ≈ 6,0 × 1,67 ≈ 10,0 m³/h

The key finding

An identical scale reading at atmospheric pressure and at 2 bar gauge pressure does not automatically represent the same quantity of gas.

For an actual measuring point

the final calculation should be performed using the actual:

• scale conditions,
• gas data,
• process conditions,
• instrument data

.

Pressure regulator upstream or downstream of the flowmeter?

In gas supply systems, a pressure regulator or control valve is often located in the immediate vicinity of the variable area flowmeter.

Its position is important

because it determines which pressure actually exists:

inside the measuring tube

.

A flowmeter upstream of a throttling valve

can, for example, operate at a significantly higher pressure than an instrument installed downstream of the pressure regulator.

For sizing, it is therefore not sufficient

to know only the cylinder pressure or compressor pressure.

What is required

is the actual operating pressure:

at the variable area flowmeter

With fluctuating backpressure

the gas density at the measuring instrument can also change.

This can cause the indication to fluctuate or become systematically affected.

Considering the pressure loss of the variable area flowmeter

A variable area flowmeter also causes a pressure loss.

For gases

the supply pressure alone is therefore not relevant.

It must be ensured

that the available differential pressure is sufficient for:

• the measuring instrument,
• the piping,
• the valves,
• downstream consumers

.

For the SITRANS FVA250

Siemens specifies as a boundary condition that the minimum operating pressure should be greater than twice the respective pressure loss.

At very low gas pressures

this point can therefore already become relevant during instrument selection.

Mounting position and flow direction

The classic variable area principle uses gravity as part of the force equilibrium.

For the SITRANS FVA250, the specified mounting position is

vertical

with flow direction

from bottom to top

.

An incorrect mounting position changes the force balance and can result in an incorrect indication.

During installation, the following should also be ensured

• mechanical pipe stresses are avoided,
• vibrations are reduced,
• process connections are correctly aligned

.

Pulsation and fluctuating indication with gases

Gas lines can exhibit pronounced pressure and flow fluctuations due to compressors, regulators or rapidly switching valves.

This can cause the float to

• oscillate,
• jump,
• fail to reach a stable position.

For the SITRANS FVA250, Siemens generally recommends damping for gas measurements

or particularly where pressure surges, turbulence or other instabilities occur.

A strongly fluctuating indication

should therefore not immediately be interpreted as:

a measuring instrument error

Instead, it should first be checked

• whether the gas pressure is stable,
• whether the control valve is oscillating,
• whether pulsations are present,
• whether the flow is being increased slowly.

Selecting the correct measuring range

A variable area flowmeter should not be selected solely according to the maximum possible gas flow rate.

The normal operating range

should use a sufficiently readable part of the scale.

For the SITRANS FVA250

Siemens specifies a measuring range turndown of:

1:10

Example

If an application normally requires:

8 … 10 Nm³/h

a measuring instrument with:

0 … 100 Nm³/h

is unnecessarily oversized in many cases.

A more suitable scale

improves:

• readability,
• resolution,
• detection of small flow changes.

Nevertheless, some reserve is required

for:

• maximum operation,
• process fluctuations,
• startup conditions.

Typical errors with variable area flowmeters for gases

Observation	Possible cause	Recommended check
Indication does not match expected gas consumption	Scale designed for different pressure or temperature conditions	Compare scale reference conditions with operating data
Measured value changes after increasing line pressure	Changed gas density	Check absolute pressure and required correction
Standard volume and operating volume are confused	Unclear flow unit	Determine the reference condition of the unit
Conversion produces clearly incorrect values	Gauge pressure used instead of absolute pressure	Take pabs = pe + patm into account
Temperature correction is implausible	Degrees Celsius entered directly into the ratio	Convert temperature to Kelvin
Instrument was designed for air but is measuring a different gas	Different gas density and viscosity	Recalculate for the gas type or redesign the scale
Float fluctuates strongly	Pulsating gas flow or pressure fluctuations	Check pressure regulation and damping
Float remains unstable	Operating pressure too low or unfavorable flow conditions	Check pressure loss and operating pressure
Indication is constantly shifted	Incorrect reference conditions	Compare scaling data with the actual process
Flow indication is correct only at one particular operating pressure	Direct-reading scale was designed for exactly this pressure	Check the application data used for the original sizing
Indication remains at the lower end of the scale	Measuring range selected too large	Consider a smaller measuring range

Which data are required for sizing?

For reliable sizing of a variable area flowmeter for gases, the process data should be specified as completely as possible.

1. Gas type

For example:

• air,
• nitrogen,
• argon,
• carbon dioxide,
• hydrogen,
• natural gas,
• gas mixture.

2. Required flow range

For example:

2 … 20 Nm³/h

3. Required flow unit

It must be defined whether the indication is to show, for example:

• l/h,
• m³/h operating conditions,
• Nl/min,
• Nm³/h

.

4. Reference condition

For standard or reference volume units, the temperature and pressure of the reference condition must be defined.

5. Operating pressure at the measuring instrument

What matters is:

pressure directly at the measuring point

and not merely the pressure of the upstream supply.

6. Gas temperature

The following should be specified:

• normal temperature,
• minimum temperature,
• maximum temperature

.

7. Process connection and nominal size

These must match the piping and the required measuring range.

8. Materials

The wetted materials must be compatible with the gas.

9. Process dynamics

The following should be taken into account:

• pulsations,
• rapid valve movements,
• compressors,
• strongly changing backpressure.

10. Signal transmission

If the flow rate is not only to be read locally, it must be clarified whether:

• limit switches,
• transmitters,
• electrical remote transmission

are required.

Practical case: Nitrogen supply at elevated pressure

In a production plant, nitrogen is to be distributed to several consumers. The existing variable area flowmeter was originally designed for gas pressure close to atmospheric pressure. After a modification to the plant, however, the measuring point is operated downstream of a pressure regulator at a significantly higher pressure.

The operator observes

that the previously familiar scale values no longer correspond to the actual nitrogen consumption.

During the analysis, the following data are first recorded

• gas type: nitrogen,
• required standard volumetric flow,
• operating pressure at the flowmeter,
• gas temperature,
• reference conditions of the existing scale.

The analysis shows

that the original scale was designed for a significantly lower gas density.

The higher gas density under the new operating conditions

changes the force equilibrium at the float and therefore the relationship between:

float position ↔ gas flow rate

Simply using the old scale value

is therefore not permissible.

For permanent operation of the system

the variable area flowmeter is sized to match:

• nitrogen,
• actual operating pressure,
• actual gas temperature,
• required standard volumetric flow unit

.

Result

With application-specific scaling, the operator can subsequently read the required gas flow directly without having to perform a manual pressure and temperature correction for every measured value.

Siemens SITRANS FVA250 at ICS Schneider

For industrial gas applications, ICS Schneider offers the:

Siemens SITRANS FVA250 variable area flowmeter

The FVA250 operates according to the variable area principle

and is suitable for:

• liquids,
• gases,
• steam.

ICS specifies, among other things, the following features

• robust all-metal design,
• impact-resistant housing cover,
• use at high pressures and temperatures,
• suitability for corrosive and flammable media depending on the version,
• product and percentage scales,
• contamination-resistant float guide,
• optional heating or cooling jacket,
• optional transmitter,
• optional limit switches.

Particularly relevant for gas flow measurements

is the possibility of adapting the scale to the specific application.

For the reference measuring-range data for gases, Siemens specifies

ρ = 1,293 kg/m³

at:

0 °C

and:

pe = 0 bar

The measuring range turndown is

1:10

For gases, Siemens specifies a measuring accuracy of

±2,0 % according to VDI/VDE 3513-2 at qG = 50 %

The specified mounting position is

vertical / flow from bottom to top

Depending on the version

different:

• nominal sizes,
• pressure ratings,
• materials,
• temperature ranges,
• measuring ranges

are available.

This makes the FVA250 particularly suitable

for industrial gas flow measurements where:

gas type + operating pressure + temperature + required scale reference

are to be taken into account during the sizing process.

Conclusion

When sizing a variable area flowmeter for gases, it is not sufficient to know only the required flow range. Since gas density depends directly on pressure, temperature and gas type, these parameters must already be taken into account when sizing the measuring instrument.

Operating volume and standard volume are different quantities

m³/h operating conditions ≠ Nm³/h

The reference condition must be clearly defined

In particular, the reference temperature and reference pressure form part of every clearly defined standard volumetric flow value.

Absolute pressure is decisive for pressure calculations

pabs = pe + patm

Temperatures must be entered as absolute values

T [K] = t [°C] + 273,15

The normal gas-state conversion must not be confused with correcting the variable area flowmeter scale

The float position itself depends on gas density. This is why a square-root relationship appears in scaling or approximate correction.

For new measuring points, an application-specific product scale is the better solution

If the gas type, operating pressure and temperature are known, the instrument should preferably be sized directly for these conditions.

The SITRANS FVA250 provides an industrial solution for this purpose

with a robust all-metal design, different process versions and product or percentage scales.

For practical applications

Define the gas type → determine the required flow range → clarify whether operating volume or standard volume is to be indicated → define the reference condition → determine the operating pressure directly at the measuring instrument → convert pressure to absolute pressure → record gas temperature → consider temperature in Kelvin → check gas density and scaling conditions → select measuring range and nominal size → consider pressure loss → ensure vertical mounting position → take pulsations and damping into account for gases → order a suitable product scale → plausibility-check the measured value after commissioning.

FAQ: Correctly Sizing Variable Area Flowmeters for Gases

Why must the pressure be specified for a variable area flowmeter used with gas?

Because gas density changes with pressure, and gas density in turn influences the position of the float.

Why must the gas temperature also be known?

Gas density decreases as absolute temperature increases. This also changes the relationship between float position and flow rate.

What does Nm³/h mean?

Nm³/h describes a gas volumetric flow referenced to defined standard conditions.

Is Nm³/h the same as m³/h?

No. m³/h can describe an actual operating volumetric flow, whereas Nm³/h has been converted to defined pressure and temperature conditions.

Which standard conditions apply to Nm³/h?

0 °C and 1,01325 bar absolute are commonly used. However, the specific reference condition should always be explicitly stated or checked.

Why must I not use gauge pressure for the conversion?

Gas density and gas equations are based on absolute pressure. Atmospheric pressure must therefore be added to the indicated gauge pressure.

How do I convert gauge pressure to absolute pressure?

Approximately using pabs = pe + patm.

What absolute pressure corresponds to 5 bar gauge pressure?

At approximately 1,013 bar atmospheric pressure, this corresponds to about 6,013 bar absolute.

Why must temperature be entered in Kelvin?

Gas equations use absolute temperature ratios. Therefore, T [K] = t [°C] + 273,15.

How many Kelvin correspond to 20 °C?

293,15 K.

What happens to gas density when pressure increases?

At constant temperature, gas density increases with increasing absolute pressure.

What happens to gas density when temperature increases?

At constant pressure, gas density decreases as temperature increases.

Why does gas density change the indication of a rotameter?

Because the force equilibrium of the float is determined, among other things, by buoyancy and flow forces, which depend on the density of the medium.

Can I use a rotameter designed for air with nitrogen?

Only after verification and corresponding correction or redesign. Even similar gases have different densities.

Can I use an air rotameter for CO₂?

Not without adjustment. The significantly different gas density changes the relationship between flow rate and float position.

Can I simply use the ideal gas equation to correct the rotameter indication?

Not directly. Pure gas-state conversion and correction of a variable area flowmeter scale are two different operations.

Why does the scale correction contain a square root?

Because the relationship between gas density, flow forces and the equilibrium position of the float is not linear with volumetric flow.

Is the square-root formula always exact?

No. It is an approximation. For accurate sizing, gas type, viscosity, float geometry, Reynolds number and real gas behavior may be relevant.

When should a new scale be designed?

If the gas type or operating conditions permanently differ significantly from the original scaling conditions, an appropriate redesign is preferable.

Which pressure is important for sizing?

The actual pressure at the variable area flowmeter or within the measuring section is decisive.

Is it sufficient to specify the compressor pressure?

No. Pressure regulators, valves and line losses can result in a significantly different pressure at the measuring instrument.

Does backpressure play a role?

Yes. Variable backpressure can change the pressure and therefore the gas density within the measuring instrument.

Does a variable area flowmeter cause a pressure loss?

Yes. The respective pressure loss depends on the instrument, measuring range and version and must be taken into account during system planning.

How must the SITRANS FVA250 be installed?

Siemens specifies a vertical mounting position with flow from bottom to top.

Why does the float fluctuate when measuring gas?

Possible causes include pulsating flow, pressure fluctuations, regulator movements, turbulence or rapid valve movements.

Is damping useful when measuring gases?

Yes. Siemens generally recommends damping for gas measurements with the FVA250 or under unstable flow conditions.

What measuring range turndown does the SITRANS FVA250 provide?

Siemens specifies a turndown ratio of 1:10 for the measuring ranges.

How accurately does the SITRANS FVA250 measure gases?

Siemens specifies a measuring accuracy of ±2,0 % according to VDI/VDE 3513-2 at qG = 50 %.

For which media is the SITRANS FVA250 suitable?

ICS specifies liquids, gases and steam.

Can the SITRANS FVA250 be used at high pressures?

Yes. ICS explicitly describes the instrument as suitable for high pressures and high temperatures. The permissible pressure rating depends on the specific instrument version.

Can the SITRANS FVA250 also be used with corrosive media?

ICS specifies corresponding versions for corrosive media. The specific material selection must be suitable for the respective medium.

Does the SITRANS FVA250 provide electrical signal transmission?

Yes. ICS specifies transmitters and limit switches as available options.

Are different scales available for the SITRANS FVA250?

Yes. ICS specifies product and percentage scales.

Which information should I provide when requesting a gas rotameter?

At minimum, the gas type, required flow range, required unit, reference conditions, operating pressure at the measuring instrument, gas temperature, nominal size or connection, material requirements and, where applicable, required electrical signals.

Where can I find the SITRANS FVA250 at ICS Schneider?

Further information can be found under Siemens SITRANS FVA250 Variable Area Flowmeter at ICS Schneider.

Where can I find additional variable area flowmeters at ICS Schneider?

An overview can be found under Variable Area Flowmeters at ICS Schneider.

Where can I find additional flow measurement technology at ICS Schneider?

An overview can be found under Flow Measurement Technology at ICS Schneider.