Reference and Flow Conversions
Applicable to following sensors
All SFMs
Key content▪
Concept of mass flow vs. volumetric flow▪
Conversion between different reference conditions▪
Conversion from mass-flow to volumetric-flow

SummaryThis application note explains the difference between mass flow and volumetric flow.
Depending on the industry and manufacturer of flow meters, the reference conditions are different and flow
values cannot be compared without converting them to the same reference conditions. The conversion between
different reference conditions and from mass flow to volumetric flow under consideration of the environmental
conditions of temperature, humidity and pressure are outlined in this document.

1 Introduction
Gas is a well compressible media, and the gas density therefore depends on the pressure and temperature of thegas. As such, a fixed volume of gas contains a different number of gas molecules, varying with temperature andpressure. To uniquely define a specific gas flow, which is a measure of a volume of gas per unit of time, it isnecessary to reference the conditions under which the measurement is performed. Depending on the industry
and the manufacturer of flow meters, these reference conditions are different and flow values can often notdirectly be compared without converting them to identical reference conditions.
Gas flow can either be measured in units of volumetric flow or mass flow.
Volumetric flow
Volumetric flow refers to a measured gas volume per unit of time under the referenced pressure and temperature
conditions. The most common units are “liters per minute [l/min]” or “actual cubic feet per minute [acfm]”.
Mass flow or standard volumetric flow
Standard volumetric flow refers to the volumetric flow at standard conditions defined for temperature andpressure. Common units are “standard liters per minute [slm]”, “standard cubic centimeters per minute [sccm]” or“norm liters per minute [ln/min]”.
Because standard volumetric flow is referenced to a defined temperature T and pressure p, the number ofmolecules n in the volume V can be calculated using the ideal gas law (p·V = n·k·T). In other words, standard
volumetric flow refers to the number of molecules per unit of time and therefore to the mass per unit of time. For agiven gas, a sensor measuring volumetric flow at standard conditions will deliver the same readings as a mass
flow sensor.
SFMxxx mass flow meters
Mass flow meters of the SFMxxx series are based on the thermal flow measurement principle and provide a mass
flow output in slm, which is a mass flow unit. For example, 1 standard litre per minute (slm) means that themeasured mass flow corresponds to a volumetric flow of 1 litre per minute under standard conditions. Sensirion’s
flow meters with a flow value in units of slm or sccm are defined at standard conditions of 20°C and 1013mbar(please refer to the specific datasheets).
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Applications
In many applications mass flow is the desired quantity instead of volumetric flow. For example, in heating
applications the calorimetric heating value, i.e. the number of gas molecules, is more important than the actual
volumetric flow. Because of its thermal measurement principle Sensirion’s SFMxxx flow meters are intrinsicallymass flow meters.
In respiratory applications volumetric flow is typically of interest instead of the mass flow. The reason is thathuman lungs have a fixed volume and will contain a varying mass flow volume (a different number of molecules)
depending on the ambient conditions such as pressure/altitude, temperature, and relative humidity. Chapter 3
explains the conversion from mass flow to volumetric flow for the SFMxxx series.

2 Conversions between Different Reference Conditions
Standard flow rate (e.g. slm) is the equivalent volumetric flow rate of the gas at the reference conditions(temperature and pressure). Although units such as slm or sccm look like a volumetric measurement they are amass flow unit and for a given medium this corresponds to the number of molecules per unit of time.
All Sensirion flow meters with a flow output in slm or sccm are defined at the reference conditions of 20°C and1013 mbar, for flow meters with outputs in norm liters per minute (typically SFM54xx) the reference condition is0°C and 1013 mbar.
Mass flow rates at different reference conditions can easily be converted into each other with the following
equation:

𝑸𝑹𝑪𝟏 = 𝑸𝑹𝑪𝟐 ∗ (QRC1
QRC2
TRC1
TRC2
PRC1
PRC2

standard flow rate with reference conditions 1standard flow rate with reference conditions 2
reference temperature 1
reference temperature 2
reference pressure 1
reference pressure 2© Copyright Sensirion AG, Switzerland

2/6𝑻𝑹𝑪𝟏
𝑷𝑹𝑪𝟐)∗()𝑻𝑹𝑪𝟐
𝑷𝑹𝑪𝟏

3 Conversions from Mass Flow to Volumetric FlowIn respiratory applications volumetric flow instead of mass flow is typically of interest. Figure 1 below depicts thechange of the gas properties often encountered:▪

In ventilation, the inspiratory sensor measures a gas flow at condition 0, which is then humidified anddelivered to the patient at gas condition 1 (often equal to BTPS). In the absence of a humidifier, the lungwould bring the gas to BTPS conditions and cause the gas to expand in the same way. Note that byhumidification water molecules are added to the gas and thus the gas volume and flow are increased.

▪

In spirometry, ambient air is measured (condition 0) and then inhaled. Again, in the lung the gas condition ischanged to BTPS (condition 1) and thus expands.

Condition 0▪ pabs▪ T0▪ RH0∆TFlow V0

Flow V1∆RH

Condition 1▪ pabs▪ T1▪ RH1

Figure 1Schematic of gas flow at various conditions including the change of temperature andhumidity

3.1 General Formula for Volumetric Flow
With the following equation, the sensor reading (in slm) at one condition (“sensor”) can be converted into a
volumetric flow at a different condition (“target”) while the gas temperature and relative humidity can change
between these two conditions:𝑉̇ =𝑇𝑡𝑎𝑟𝑔𝑒𝑡
Q
101325
1 + 𝐶𝐻2𝑂 ∗ 𝑑𝑣 (𝑇𝑠𝑒𝑛𝑠𝑜𝑟 , 𝑅𝐻𝑠𝑒𝑛𝑠𝑜𝑟 ) 𝑝𝑎𝑏𝑠 − 𝑝𝐻2𝑂,𝑡𝑎𝑟𝑔𝑒𝑡 293.15

With:
𝑉̇volumetric flow of (humid) air in liters/min𝑄
mass flow reading of sensor in slm𝑝𝑎𝑏𝑠
barometric pressure in Pa
𝑝𝐻2𝑂,𝑡𝑎𝑟𝑔𝑒𝑡 partial pressure of water in Pa at target condition𝑇𝑥temperature of air in Kelvin (sensor / target condition)
𝑅𝐻𝑠𝑒𝑛𝑠𝑜𝑟 actual relative humidity at sensor condition
𝑑𝑣
absolute humidity in g/m3 at sensor condition
CH2O= 0.002; experimentally determined to be around ~0.2% per g(H2O)/m3 of added absolutehumidity.
Note: with the factor 1 + 𝐶

1

𝐻2𝑂 ∗ 𝑑𝑣 (𝑇𝑠𝑒𝑛𝑠𝑜𝑟 ,𝑅𝐻𝑠𝑒𝑛𝑠𝑜𝑟 )the sensor mass flow reading Q in slm of humid air istransformed into the corresponding a mass flow value of dry air in slm (without humidity).

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For the case of dry gases (without humidity) the above equation simplifies to:𝑉̇ = 𝑄

101325 𝑇𝑡𝑎𝑟𝑔𝑒𝑡
𝑝𝑎𝑏𝑠 293.15

With:
𝑉̇𝑄
𝑝𝑎𝑏𝑠
𝑇𝑡𝑎𝑟𝑔𝑒𝑡volumetric flow of (humid) air in liters/min
mass flow reading of sensor in slm
barometric pressure in Pa
temperature of air in Kelvin at target

The absolute humidity can be derived from the relative humidity and temperature with the following equation:
𝑅𝐻𝑚·𝑇
100% 𝐴 · 𝑒𝑥𝑝 (𝑇𝑛 + 𝑇)
𝑑𝑣 (𝑇, 𝑅𝐻) = 216.7 []273.15 + 𝑇
With:𝑑𝑣𝑇𝑅𝐻𝑚𝑇𝑛𝐴

absolute humidity in g/m3
actual temperature in °C
actual relative humidity
17.62
243.12 °C
6.112 hPa

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3.2 Calculator
The excel calculator in AppNote SFM-26 “Reference And Flow Conversions Calculator” with the equations
described above allows to determine the scaling factor to convert the mass flow sensor reading into thevolumetric flow. This calculator can be downloaded here
Example 1: Convert Mass Flow of Dry Air to Volumetric Flow at BTPS Conditions
Considering a Sensirion mass flow sensor is positioned on the inspiratory side of a ventilator and exposed to drywall gas at ambient temperature, e.g. Tsensor = 20°C and RHsensor = 0%. The gas is then humidified and warmed tobody core temperature, hence Ttarget = 37°C and RHtarget = 100%. As such, water vapor is added to the dry gas
and the gas temperature is increased. Both circumstances result in a volume expansion.
The scaling factor to convert the mass flow reading of the sensor to volumetric flow at BTPS conditions can becalculated based on the values above using the calculator tool in the following way:

Figure 2. Conversion of mass flow at dry air condition to volumetric flow at BTPS using the calculator tool
Example 2: Convert Mass Flow of Ambient Air to Volumetric Flow
Considering the Sensirion mass flow sensor is positioned downstream of a blower and exposed to ambient air atTsensor = 25°C and RHsensor = 50%. To convert the measured mass flow to a volumetric flow (without additional
humidification of the gas), we can simply insert Ttarget = Tsensor and RHtarget = RHsensor into the calculator:

Figure 3. Conversion of ambient air mass flow to volumetric flow
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4 Revision History
Date
Jan 2021
Sept 2021

Author
LOEH
LOEH

Version
1.0
1.1

Changes
Initial release
Corrected factor CH2O = 0.002

5 Headquarters and Subsidiaries
SENSIRION AG
Laubisruetistr. 50
CH-8712 Staefa ZH
Switzerland

Sensirion Korea Co. Ltd.
phone: +82 31 337 7700 3
info-kr@sensirion.com
www.sensirion.co.kr

phone: +41 44 306 40 00
fax:+41 44 306 40 30
info@sensirion.com
www.sensirion.com

Sensirion China Co. Ltd.
phone: +86 755 8252 1501
info-cn@sensirion.com
www.sensirion.com.cn

Sensirion Inc., USA
phone: +1 805 409 4900
info-us@sensirion.com
www.sensirion.com

Sensirion AG (Germany)
phone: +41 44 927 11 66
info@sensirion.com
www.sensirion.com

Sensirion Japan Co. Ltd.
phone: +81 3 3444 4940
info-jp@sensirion.com
www.sensirion.co.jp© Copyright Sensirion AG, Switzerland

To find your local representative, please visit
www.sensirion.com/contact

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