Specification

The present invention relates to a method for controlling a mass flow of a fluid in a bioanalytical device as well as to a bioanalytical device for conducting the method according to the present invention.

The present invention can be used in the field of particle collection and sampling as well as analysis of particles of all kinds. Especially, it is related to bioanalytical devices such as e.g. instruments for characterization of gas or air quality as necessary in food and beverage industries or clean environments such as cleanrooms and manufacturing environments. Examples for such clean environments are production lines in the pharmaceutical industries, where air quality has to be constantly monitored and tested.

Bioanalytical devices in form of microbial air samplers are a specific type of air monitoring devices that focus on the collection of particles on a microbial growth medium - usually in form of a petri dish filled with agar media or similar. After collection of particles from the gas/air on such a medium plate, the plate is incubated for several hours or even days in order to let collected living microorganisms grow into visible colonies for subsequent counting and analysis.

There generally exist regulatory limits on how many and which organisms are tolerable in a specific environment and in case limits are exceeded, production lots of pharmaceuticals are discarded for example. Hence, analysis of the air quality with a focus on microbial contamination is a critical quality indicator for product release in multiple large industries.

High measurement precision can only be achieved when high system performance (stable air flow during the measurement and accurate quantification of the sampled gas volume) come together with well-trained personnel as well as appropriate cleaning and handling procedures.

Air sampling devices often incorporate miniature sensors for gas flow. These sensors typically measure mass flow but not volumetric flow and depend on ambient conditions (absolute pressure, temperature, humidity level), the ratio between air/gas mass and volume can change significantly. Hence, when the determination of accurate gas volume flow rates is required one or more of the afore-mentioned parameters need to be incorporated for high accuracy.

Any particle collector and/or counter for gaseous media relies on two critical functions, namely quantifying the particulate matter, and quantifying the sampled gas volume in which the particulate matter has been present.

US2015355000A1 discloses a method of controlling a volumetric flow rate of a fluid flow through a particle impactor system, the method comprising the steps of: letting said fluid flow through a plurality of intake apertures of a sampling head of said particle impactor system; determining a flow rate of said fluid; determining ambient pressure; determining said volumetric flow rate as a function of said flow rate of said fluid and said ambient pressure; and controlling the fluid flow in said particle impactor system using said volumetric flow rate.

However, controlling the volume flow usually requires to continuously compute this quantity from, e.g., a mass flow, thus creating a disadvantageous constant load onto the computing unit of the device.

Therefore, based on the above, the problem to be solved by the present invention is to provide a method for controlling a fluid flow in a bioanalytical device, particularly in a microbial air sampler, that is improved regarding the above-stated difficulty.

This problem is solved by a method having the features of claim 1 and a bioanalytical device having the features of claim 15.

Preferred embodiments of these aspects of the present invention are stated in the corresponding sub claims and are also described below.

According to claim 1 , a method for controlling a mass flow of a fluid in a bioanalytical device is disclosed, the bioanalytical device comprising a control unit and a fluid flow generating device for generating a fluid flow of the fluid, wherein the method comprising the steps of: a) inputting a desired volume flow set point of the fluid flow into the control unit (and particularly generating the fluid flow by means of the fluid flow generating device), b) automatically calculating a mass flow set point of the fluid flow with the control unit, the mass flow set point corresponding to said volume flow set point, c) measuring an actual mass flow of the fluid flow with a mass flow sensor of the bioanalytical device, and d) adjusting the flow generating device by the control unit to let the actual mass flow approach the mass flow set point.

Particularly, sensors for mass flow of fluids, particularly gases (either direct or in a bypass configuration to measure differential pressure across the bypass) are available also in miniaturized form even allowing cost-critical applications. Particularly, the mass flow sensor is a thermal mass flow sensor.

The invention allows to accurately control the mass flow sampled by a bioanalytical device using at least one mass flow sensor and particularly one or several sensors for at least two parameters out of temperature, pressure and relative humidity of the sampled fluid. Preferably, said sampled fluid is air that may be contaminated with contaminants/impurities such as particulate matter, bacteria etc.

According to a preferred embodiment of the present invention, the method further comprises the step of e) repeating steps c) and/or d).

According to a preferred embodiment, step d) can be conducted at a longer interval (i.e. with slower rate) than the interval at which step c) is conducted.

Furthermore, according to a preferred embodiment of the method, step b) is conducted only once before starting the fluid flow using the fluid flow generating device.

According to a further embodiment, step d) further comprises automatically recalculating the mass flow set point of the fluid flow corresponding to said volume flow set point at a pre-defined interval. In a preferred embodiment, said pre-determined interval is longer than an interval at which step c) is conducted, i.e., the interval at which controlling of the fluid flow generating device takes place.

According to a further embodiment, step b) further comprises measuring a pressure of the fluid and/or a temperature of the fluid and/or a relative humidity of the fluid, and using the measured pressure of the fluid and/or the measured temperature of the fluid and/or the measured relative humidity of the fluid for automatically determining the mass flow set point of the fluid flow corresponding to said volume flow set point.

According to another preferred embodiment, step b) further comprises measuring the pressure, the temperature and the relative humidity of the fluid (e.g. by using said sensors or single sensor device described further below) and determining an actual density of the fluid P fluid , and determining the mass flow set point M _set of the fluid flow based on said volume flow set point V _set and said actual density, particularly according to the formula

Mset ~ P luidVset-

In another preferred embodiment, automatically recalculating the mass flow set point is conducted only in case the temperature has changed at least by a pre-defined amount and/or in case the pressure has changed at least by a pre-defined amount and/or the relative humidity has changed at least by a predefined amount.

In this fashion, the respective embodiments of the present invention allow to reduce computational load on the controlling unit in an advantageous manner, namely e.g., by assuming that temperature, pressure and/or relative humidity change rather slowly, so that recalculation of the mass flow set point can be performed at a longer interval than the loop controlling the fluid flow. Alternatively, only upon a change of temperature, pressure and/or relative humidity that is deemed significant, a recalculation of the mass flow set point may be conducted. Also, if changes in environmental conditions are known to be negligible or insignificant considering the duration and required accuracy of the flow, the mass flow set point may even be calculated only once initially, which further reduces computational load.

Further, according to a preferred embodiment, the pressure is measured with a pressure sensor arranged in a flow channel of the bioanalytical device. Alternatively, the pressure sensor can be arranged to measure the pressure of an ambient environment of the bioanalytical device.

Likewise, in a preferred embodiment, the temperature is measured with a temperature sensor arranged in the flow channel of the bioanalytical device. Alternatively, the temperature sensor can be arranged to measure the temperature of an ambient environment of the bioanalytical device.

Further, in a preferred embodiment, the relative humidity is measured with a relative humidity sensor arranged in the flow channel of the bioanalytical device. Alternatively, also the relative humidity sensor can be arranged to measure the relative humidity of an ambient environment of the bioanalytical device in a preferred alternative embodiment.

Regarding the respective sensor, several or all of: the pressure sensor, the temperature sensor, the relative humidity sensor, can be integrated into a single sensor device according to a preferred embodiment of the present invention. This single sensor device is then configured to measure the respective quantity, i.e., several or all of said pressure, temperature, relative humidity.

Particularly, according to an embodiment, the flow channel can comprise a constriction for generating a pressure drop in the flow channel (i.e., across the constriction).

According to yet another embodiment of the method according to the present invention, the (e.g. thermal) mass flow sensor comprises a conduit for passage of a partial flow of the fluid flow through the conduit of the mass flow sensor, the conduit extending between a first and a second port.

According to preferred embodiment, the first port is in flow connection with the flow channel.

According to a preferred embodiment, the second port is in flow connection with the flow channel. Alternatively, in a preferred embodiment, the second port preferably opens outside the flow channel of the bioanalytical device to an ambient environment of the bioanalytical device. Furthermore, according to a preferred embodiment, the first port is in flow connection with a location upstream said constriction of the flow channel. Further, according to a preferred embodiment, the second port is in flow connection with a location at the constriction or downstream the constriction.

In a preferred alternative embodiment, the mass flow sensor is a thermal mass flow sensor not placed in a bypass. Here, particularly, this also means that there is no need for a constriction as the fluid (e.g. air) passes by the mass flow sensor anyway and thereby creates a temperature shift between temperature sensing elements of the flow sensor that are located up- and downstream of a heating element of the thermal mass flow sensor. Alternatively, a heating element of the thermal mass flow sensor is kept at a desired temperature and the electrical current necessary to keep the heating element on the desired temperature is determined. The more flow, the more heat is transported from the heating element and the more current is needed to heat it up to keep the temperature constant.

Furthermore, according to a preferred embodiment of the method, the fluid flow is passed through a filter of the bioanalytical device.

Furthermore, in a preferred embodiment of the method, it is automatically detected, if the filter has been arranged in the bioanalytical device. This can be achieved by utilizing the fact that the filter will form a flow resistance for the fluid flow, which can be detected by a decrease in pressure of the fluid downstream the filter and/or an increase of the pressure of the fluid upstream the filter compared to a reference value of the pressure. Thus, particularly, in an embodiment, the method comprises the further step of detecting if a filter, through which the fluid flow is to be passed, is present in the bioanalytical device, by measuring at least the pressure upstream or downstream of a position of the filter in the fluid flow and comparing the measured pressure to at least one reference value of the pressure.

According to a further preferred embodiment, a state of the filter is detected, the state being indicative of a loading of the filter with impurities present in the fluid flow.

According to a further embodiment, it is automatically detected if the filter is loaded with impurities to a certain degree so that particularly a replacement of the filter is required or beneficial. This can also be detected by measuring the pressure which will change due to the filter forming a larger flow resistance when being loaded with impurities.

According to a further embodiment, the user will be automatically notified by the bioanalytical device in case it is determined that the filter is loaded with impurities to a certain degree and therefore requires replacement or cleaning.

Furthermore, according to yet another embodiment, the user is proposed to order a replacement filter by the bioanalytical device when the filter requires replacement. Further, according to a preferred embodiment, the bioanalytical device is configured to provide a link to a URL of a provider of a replacement filter for ordering thereof.

Furthermore, according to yet another embodiment, an increase in flow resistance in the flow channel upstream a location where the pressure is measured is detected. Preferably, in an embodiment, the user is alerted that said inlet might be blocked (e.g., by a cover placed on a lid of the bioanalytical device, the lid comprising said inlet).

According to a further aspect of the present invention, a bioanalytical device (particularly a microbial air sampler) is disclosed particularly for conducting the method according to the present invention, the bioanalytical device comprising:

- a housing enclosing a flow channel,

- a fluid flow generating device for generating a fluid flow in the flow channel,

- a control unit for controlling the fluid flow generating device,

- a mass flow sensor configured to measure an actual mass flow of the fluid flow wherein the control unit is configured to receive a desired volume flow set point of the fluid flow as an input, to calculate a mass flow set point of the fluid flow corresponding to said volume flow set point, and to adjust the flow generating device to let the actual mass flow approach the mass flow set point.

According to a preferred embodiment of the bioanalytical device, the bioanalytical device comprises a pressure sensor configured to measure a pressure of the fluid.

Furthermore, according to a preferred embodiment of the bioanalytical device, the bioanalytical device comprises a temperature sensor configured to measure a temperature of the fluid.

Further, according to a preferred embodiment of the bioanalytical device, the bioanalytical device comprises a relative humidity sensor configured to measure a relative humidity of the fluid.

According to a preferred embodiment, the pressure sensor is arranged in the flow channel or is arranged outside the flow channel to measure said pressure in an ambient environment of the housing of the bioanalytical device.

Furthermore, according to a preferred embodiment, the temperature sensor is arranged in the flow channel or is arranged outside the flow channel to measure said temperature in an ambient environment of the housing of the bioanalytical device.

Furthermore, according to a preferred embodiment, the relative humidity sensor is arranged in the flow channel or is arranged outside the flow channel to measure said relative humidity in an ambient environment of the housing of the bioanalytical device. In a preferred embodiment of the bioanalytical device several or all of: the pressure sensor, the temperature sensor, the relative humidity sensor is integrated into a single sensor device configured to measure the respective quantity, i.e., several or all of said pressure, temperature, relative humidity.

Furthermore, in a preferred embodiment, the flow channel comprises a constriction to generate a pressure drop across the constriction.

Further, in a preferred embodiment of the bioanalytical device, the mass flow sensor comprises a conduit for passage of a partial flow of the fluid flow through the conduit of the mass flow sensor, the conduit having a first port (e.g. inlet) in flow connection with the flow channel of the bioanalytical device and a second port (e.g. an outlet), wherein the second port is in flow connection with the flow channel (particularly in the vicinity of the constriction or downstream said constriction) or opens outside the flow channel to an ambient environment of the bioanalytical device. In an alternative embodiment, the mass flow sensor is a thermal mass flow sensor being in thermal contact with the fluid flow in the flow channel to measure a mass flow of the latter as e.g. described above.

Furthermore, in a preferred embodiment of the bioanalytical device, the control unit is configured to use the measured pressure of the fluid and/or the measured temperature of the fluid and/or the measured relative humidity of the fluid for determining the mass flow set point of the fluid flow corresponding to said volume flow set point.

According to a preferred embodiment, the control unit is configured to determine the actual density of the fluid (e.g., air) using the measured pressure, measured temperature and measured relative humidity of the fluid and to determine the mass flow set point M _set of the fluid flow based on said volume flow set point V _set and said actual density Pf _luid , particularly according to the formula

Mset ~ Pfiuid ' set

Furthermore, according to an embodiment of the bioanalytical device, the housing is configured to accommodate a carrier carrying a moist medium in the internal space of the housing so that the flow channel extends along the moist medium.

In a preferred embodiment of the bioanalytical device, the moist medium is a moist growth medium for promoting microbial growth, wherein here the bioanalytical device is a microbial air sampler.

Furthermore, in a preferred embodiment, the flow channel of the bioanalytical device extends from an inlet of the housing to an outlet of the housing. In a preferred embodiment of the bioanalytical device, the fluid flow generating device is further configured to provide the fluid flow through the flow channel so that the fluid flow passes the moist medium carried by the carrier when the carrier is arranged in the internal space, wherein the bioanalytical device is configured to pass the fluid flow along the moist medium when the carrier is arranged in the internal space such that particulate matter contained in said fluid flow settles on the moist medium (e.g. said growth medium).

According to yet another preferred embodiment of the bioanalytical device, the fluid flow generating device for generating said fluid flow is a fan comprising a rotating arrangement of blades, wherein adjusting the fluid flow generating device comprises to adjusting a rotation speed of the arrangement of blades.

Further, according to a preferred embodiment of the bioanalytical device, the housing comprises an openable lid to allow access to said internal space, so that the moist medium can be accommodated in said internal space in an open state of the lid and is enclosed by the housing in a closed state of the lid, wherein said inlet is formed in the lid in particular.

Furthermore, in a preferred embodiment, the bioanalytical device (e.g., microbial air sampler) comprises a filter arranged upstream said outlet of the housing and particularly downstream the mass flow sensor and sensor(s) for measuring temperature and/or pressure and/or relative humidity. Presence and/or Loading of the filter can be detected by the bioanalytical device as described above.

Particularly, the bioanalytical device according to the present invention can be further characterized in preferred embodiments by the features and embodiments described above in conjunction with the method according to the present invention. Particularly, the bioanalytical device is configured to conduct the method according to the present invention.

The present invention proves to be advantageous in that calculation of the desired mass flow set point can be based on absolute pressure and temperature as well as optionally relative humidity. Furthermore, the approach according to the present invention, namely achieving a desired volumetric flow by regulating for its corresponding target mass flow, significantly reduces computational effort.

Furthermore, while the fluid flow is ongoing, comparing pressure with threshold values (e.g., values characteristic for the instrument type or pressures present during calibration of the instrument) allows one to make predictions about the state of the instrument.

Further, advantageously, due to being able to efficiently control the fluid flow in the bioanalytical device, an increased or decreased pneumatic resistance in the system - such as caused by aging and partial blockage of an integrated filter- can be compensated. Furthermore, the invention in principle allows controlling the bioanalytical device for both mass flow and volume flow.

Further, the invention allows to achieve a higher precision over a wide temperature and/or humidity range without significantly increasing cost and compactness of the solution (temperature and humidity sensors are affordable and require only small footprint on a printed circuit board).

The invention further allows simplifying the implementation of a control logic (compared to continuously converting a mass flow to a volume flow). Regardless of running mass flow or volumetric flow, in both cases the control loop is controlling mass flow.

According to yet another aspect of the present invention, a method for detecting a filter and/or a state of a filter in a bioanalytical device is disclosed, the bioanalytical device comprising a flow generating device for generating a fluid flow in a flow channel comprised by the bioanalytical device, the method comprising the steps of: generating a fluid flow in the flow channel and automatically detecting the presence or absence of a filter of the bioanalytical device in the flow channel and/or automatically detecting a state of the filter, the state being indicative of a loading of the filter with impurities present in the fluid flow.

According to yet another aspect of the present invention, a bioanalytical device, particularly for conducting said method for detecting said filter and/or state is disclosed, comprising:

- a housing enclosing a flow channel,

- a fluid flow generating device for generating a fluid flow in the flow channel,

- a filter configured to be positioned in the flow channel (particularly such that the fluid flow can be passed through the filter), wherein the bioanalytical device is configured to automatically detect the presence or absence of the filter in the flow channel and/or to automatically detect a state of the filter, the state being indicative of a loading of the filter with impurities present in the fluid flow.

Preferably, the bioanalytical device comprises at least one pressure sensor upstream or downstream a location in the flow channel configured to receive the filter to detect said presence/absence and/or state (see also above). In the following, embodiments of the present invention as well further features and advantages and other aspects of the present invention shall be described with reference to the Figures, wherein

Fig. 1 shows a control loop of an embodiment of the method I bioanalytical device according to the present invention, Fig. 2 shows a perspective view of an embodiment of a bioanalytical device in form of a microbial air sampler,

Fig. 3 shows a schematic cross-sectional view of the microbial air sampler of Fig. 2, and

Fig. 4 shows different embodiments of a bioanalytical device regarding a configuration of the flow channel and mass flow sensor as well as temperature, pressure and relative humidity sensor(s).

Fig. 1 shows a block diagram of a preferred control loop 100 that can be used in the method / bioanalytical device 1 according to the present invention. Importantly, the invention does not aim to control the volume flow through the bioanalytical device 1 directly (convert mass flow to volume flow with current sensor readings for temperature, pressure, and humidity and adjust fan to reach a target volume flow rate), but to calculate a target mass flow (termed mass flow set point) that matches the volume flow set point at the current conditions of temperature T, pressure P and relative humidity RH. The advantage of this approach is that no matter whether one regulates to achieve a constant mass flow or volume flow, one can always use the same procedure; only the mass flow set point needs to be recalculated according to the ambient conditions.

Preferably, this invention uses a thermal mass flow sensor 4 together with sensors 5 to measure the temperature T, absolute pressure P, and optionally relative humidity RH of the sampled air. As all these sensors 5 are available in miniaturized formats, this method can be implemented not only in large devices, but is also suited for portable applications (Fig. 1).

As shown in Figs. 2 and 3, the bioanalytical device 1 can be an e.g., portable microbial air sampler (as an example of a particle monitoring system) that draws a fluid (here a gas such as air) through an inlet 16 formed by a perforated lid 14 at a top of a housing 13 of the bioanalytical device 1 . The fluid flow F flows through an integrated fluid flow generating device 3 such as a fan, a flow channel 10 forming a sensing path, and is eventually released via an outlet 17 (here on the bottom side of the sampling head). Particularly, a replaceable filter 12 can be placed upstream said outlet 17, wherein the bioanalytical device 1 can be configured to automatically detect the presence or absence of the filter 12 and/or to automatically detect a state of the filter 12, the state being indicative of a loading of the filter 12 with impurities present in the fluid flow F. Particularly, the bioanalytical device 1 can prompt the user to arrange a filter 12 in the flow channel 10 or to replace/clean the filter if necessary.

Particularly, the housing 13 is configured to accommodate a carrier 15 carrying a moist medium so that the flow channel 10 extends along the moist medium. Particularly, the moist medium is a moist growth medium for promoting microbial growth. The fluid flow generating device 3 is configured to let the fluid flow F pass through the flow channel 10 so that the fluid flow F passes the moist medium carried by the carrier 15 such that particulate matter contained in said fluid flow F settles on the moist medium (e.g. said growth medium).

The flow channel / sensing path 10 preferably comprises a thermal flow sensor 4 measuring the pressure drop along a specific portion of the flow channel 10 (this section may include elements such as a constriction 11 , a venturi configuration, an orifice, or similar) or between a specific point in the flow channel 10 and the ambient environment Pambient and sensors 5 for the parameters: temperature T, absolute pressure P and relative humidity RH. The latter parameters may be measured by a single sensor device 5 having integrated therein the functionalities to measure said parameters.

The sensor(s) 5 for P, T, RH allow determination of the current air density. The mass flow sensor(s) 4 determine the actual mass flow in the bioanalytical device 1. Requested volume flow (i.e., the volume flow set point) and the actual fluid (e.g., air) density can be used to calculate the volume flow equivalent mass flow set point. The fluid flow generating device (e.g., fan) 3 is then controlled such that the mass flow sensor signal matches the desired mass flow set point.

Furthermore, Fig. 4 shows possible embodiments of the mass flow control with different sensor configurations (a-c) and exemplary measurement workflow (d). Note that absence of one or more sensor elements in the P, T, RH sensor 5 is possible. In such a case, either simplified equations for the relationship between mass flow and volume flow can be used (see below) or pre-defined approximate values for missing sensor-values can be used (like substituting the actual humidity from a RH sensor with a fixed value of 40%RH).

According to Fig. 4 a, a thermal mass flow sensor 4 is used in a bypass configuration to measure the pressure drop along the flow channel 10. Here, the mass flow sensor 4 comprises a conduit 40 having a first port 41 (e.g. inlet) in flow connection to the flow channel 10 and a second port 42 (e.g. an outlet) being in flow connection with the flow channel 10, too. The pressure drop can be artificially enlarged using a flow constriction 11 , wherein the inlet 41 of the conduit 40 can be arranged upstream the constriction 11 , whereas the outlet 42 of the mass flow sensor’s conduit 40 can be positioned in the vicinity of the constriction 11 or downstream the constriction 11. The measuring points for temperature T, pressure P, and relative humidity RH are preferably located directly in the flow channel 10 before, after, or in parallel to the mass flow sensor 4. As indicated in Fig. 4 a, the sensor(s) 5 can alternatively also be configured to measure T, P, RH in an ambient environment of the bioanalytical device 1 . This also applies to the configurations shown in Figs. 4 b-c. Particularly, in contrast to Fig. 4 a, Fig. 4 c shows a configuration in which the thermal mass flow sensor 4 is not placed in a bypass configuration, but is in thermal contact with the fluid in the flow channel 10, wherein the fluid (e.g. air) in the flow channel 10 passes by the mass flow sensor 4 and thereby creates a temperature shift between temperature sensing elements (now shown) of the flow sensor 4 that are located up- and downstream of a heating element (not shown) of the thermal mass flow sensor 4 (see also above). Furthermore, in contrast to Fig. 4 a, Fig. 4 b shows a configuration in which the outlet 42 of the mass flow sensor’s conduit 42 opens to the ambient environment Pambient of the bioanalytical device 1.

In the following, the physical background of the invention is described, which allows the control unit to estimate a mass flow set point based on a given volume flow set point. It is to be noted, that different theories and corresponding equations may be used to compute the quantities discussed below. Particularly other equations may be used instead of the Magnus-Equation. The constants used in the respective equation may have a precision suitable for the desired level of accuracy.

When regulating to a fix mass flow, the thermal mass flow sensor is used alone. When regulating to a volumetric flow rate set point, the corresponding mass flow rate set point is determined by using the parameters temperature, pressure and humidity in order to calculate the density of the fluid (in the following air as an example) at these conditions:

With the p _air density of air, P the absolute pressure, T the temperature in Kelvin, and R _f the gas constant. The gas constant is itself dependent on the ambient conditions and can be calculated using the following equation:

Here, R _s is the gas constant for dry air with and R _d the gas constant of water vapor with 461.523 The relative humidity as determined by humidity sensors p, the absolute ambient pressure P, and the saturation vapor pressure P _sat are also to be taken into account.

Using the Magnus-equation above plain water surfaces as an approximation, the saturation vapor pressure at the current temperature T _act can be calculated with the following equation: Taking all this together, the density of air is only dependent on temperature, absolute pressure and relative humidity of the sampled air and follows this equation:

When the volume flow rate of the fluid (e.g. air) V _air is given, one can then easily convert to mass flow rate of the fluid/air M _air '.

Mair Pair ' ^air

Often however, the normalized or standardized volume flow V _{air n} ' _O rm is mentioned instead of a mass flow M _air . To convert between these units, one needs information of the standard conditions (T, P, relH) and the corresponding norm or standard density p _a ir,norm used for the conversion:

When gasses different than air are measured, mass flow rate is scaled with a gas-dependent factor c _aa .(V _air „ _n r lit J) that can itself be a function of the current sensor signal:

When air is the fluid/gas of interest and lower accuracy is needed, the relative humidity of the air can be assumed to be 0%. Then the gas constant is equivalent to the ideal gas constant:

Rf ⁼ R _S

In this case, the relationship between volume flow and mass flow (normalized volume flow) iorm IS. which may be rearranged to e.g., calculate a mass flow target based on a desired volumetric flow: