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Electronic Mass Flowmeters Flow Reference


Flow Reference Section

                                                  All shown smaller
                                                  than actual size.

                                           FMA-4109, $730, see page D-9.

   FMA-A2117, $538, see page D-19.                                             FMA1828, $655 with optional totalizer,
                                                                               FMA-TOTAL-28, $195, see page D-11

The continuing need for improved
accuracy in flow measurement of
mass related processes such as
chemical reactions and thermal         The ideal gas law defines the
transfers has resulted in the          volume a certain mass of gas will
development of electronic mass         occupy under specific conditions.
flowmeters. Thermal-type mass          For example, say a fixed mass of
flowmeters operate with minor          gas occupies a one liter container at
dependence on density, pressure,       21°C (70°F) under 1 atmosphere
and fluid viscosity. This style of     pressure. When the pressure of the
flowmeter utilizes a heated sensing    system is increased (with the
element and thermodynamic heat         temperature held constant), the
                                       volume will decrease. If the
conduction principles to determine     temperature is increased, (with the
the true mass flow rate.               volume held constant), the pressure
Understanding Mass Flow                will increase. The only constant
                                       variable is the mass of the gas; it
To understand the mass flow            does not change.
concept, it is essential to begin
                                       Mass flow is the molecular
with the relationship between mass,    measurement of the gas flow rate.
temperature and pressure. Real         This is usually measured in units of
gases roughly follow the ideal gas     mass per unit of time, as kilograms
law, which states that the pressure,   per hour. However, gas flow is          Figure 1: Insertion style mass flow
temperature and volume of a gas                                                sensor utilizes RTD sensor to
                                       usually measured in volume, such        measure the flow rate
are all interrelated.                  as liters per hour, but, since volume
                                       is dependent upon temperature and       (14.7 psia) pressure. Using these
PV = nRT, where:                                                               standards, it is possible to take an
                                       pressure, it is therefore necessary
P = pressure of the gas                to adopt standard temperature and       exact mass flow and reference it to
V = volume that the gas occupies       pressure conditions before one can      more traditional measures without
n = number of molecules (i.e., mass)   define volumetric flow rate. Usually,   losing accuracy. For example, a
R = ideal gas constant                 these conditions are specified as       226 kg (500 lb) per hour flow of
T = temperature of the gas             21°C (70°F) and 1 atmosphere            nitrogen can be translated into
standard cubic feet per minute         OPERATING PRINCIPLE                      differential (T2-T1) between the two
(SCFM) units using the following                                                sensors in a Wheatstone bridge
relationship:                          Electronic mass flowmeters and flow      circuit is measured. Since the
                                       controllers employ thermodynamic         temperature difference between the
       •                               principles to measure true mass flow
Q = m/(r)
 s           s                                                                  two sensors is directly proportional
                                       rate without the need for                to the mass flow of the gas (m), a
where:                                 temperature or pressure
(r)s = density of the gas                                                       highly accurate and repeatable flow
                                       compensation. The following is a         measurement is obtained.
       at standard conditions          brief description of the two operating
 • = mass flow rate                    principles employed: heated tube         Electronic mass flowmeters are not
m                                                                               affected by pressure or temperature
                                       and immersed probe.
Qs = standard mass flow rate                                                    changes over the specified range of
       (e.g., SCFM)                    Heated Tube                              the unit.
In many applications, only the         FMA-A2000, FMA1700/1800,                 Also, heated tube mass flowmeters
volumetric flow rate referenced to     FMA3300 and FMA-4100 Series              can accommodate virtually any
the actual pipe conditions is known.   Flowmeters                               clean gas. If the flow range remains
To convert actual cubic feet per       In these units, all or part of the gas   the same, a correlation factor (K) is
minute (ACFM) to standard              flow passes through a precision-         typically used to relate the calibration
conditions (SCFM), the following       manufactured sensing tube (Fig. 2).      of nitrogen to the actual gas. This K
relationship is used:                  Heat (Q) is applied to the gas           factor is derived experimentally or
                                       flowing through the sensor tube via      from the gas density and coefficient
Qs = Qa x (Pa /Ps) x (Ts /Ta)
                                       two externally wound resistance          of specific heat:
Pa = actual pressure
                                       temperature detectors (T1 and T2).
                                       The detectors have a dual function:
                                                                                K = (r)CP
Ps = standard pressure                 to both heat and sense the sensor-       r= gas density (g/liter)
Ts = standard temperature              tube temperature. When the molecules     CP = coefficient of specific heat
Ta = actual temperature conditions     of the gas pass through the                     (cal/gram °C)
Qa = actual mass flow rate             upstream sensor winding (T1) they
      (e.g., ACFM)                     carry away a certain amount of heat.
For example, to determine the          This process is repeated at the
standard flow rate of a gas at 100°F   downstream sensor winding (T2) but
and 100 psig, flowing at 100 ACFM:     less heat is transferred from the
                                       downstream sensor winding due to
Qs = 100 ACFM x                        the flow’s having been preheated by
(100 psig + 14.7 psia) x               the first sensor. The temperature
      (14.7 psia)

     (529.4 R)
  (459.4 + 100°F)

     Figure 2                                   POWER SUPPLY

                 T1, UPSTREAM                                                         T2, DOWNSTREAM
                 TEMPERATURE                                                           TEMPERATURE
                     SENSOR                                                                SENSOR

                                             BYPASS SENSOR TUBE


                         POWER                    BRIDGE FOR                                                 LINEAR
                         SUPPLY                  ΔT DETECTION                   AMPLIFIER                    OUTPUT

Flow Reference Section
                                                                          The flowrate of a reference gas
                                                                          (subscript “r”) and that of an actual
                                                                          gas (subscript “a”) are related as

                                                                          Qa = (Kr/Ka)Qr = (rr Cpr) Qr
                                                                                             (ra Cpa)

                                                                          Q = mass flow rate in SCCM
                                                                          Note that, in the above relationship,
                                                                          (r) and Cp are usually established
                                                                          under standard conditions.
                                                                          For example, to determine the flow
                                                                          rate of carbon dioxide (CO2) when
                                                                          the flowmeter is calibrated in
                                                                          nitrogen at 100 SCCM, the
                                                                          conversion equation is

                                                                                     rN2   CrN2
                                                                          QCO2 =         x      x QN2
                                                                                    rCO2 CrCO2

                                                                          = 1.16 x 0.249 x 100 = 77.0 SCCM
                                                                            1.84 x 0.204

                                                                          A partial listing of correction factors
                                                                          for different gases is provided on
                                                                          page D-13. Consult Engineering for
                                                                          other factors.
                                                                          Flexibility, easy maintenance, and
                                                                          excellent low-flow sensitivity are
                                                                          the major benefits of heated tube
                                                                          mass flowmeters. The addition of an
                                                                          electromagnetically controlled
                                                                          automatic valve turns the meter
                                                                          into a mass flow controller, ideal
                                                                          for any application where mass
Figure 3: Heated tube mass flow controller
                                                                          (as opposed to volumetric) flow rate
                                                                          control is desired.
                                                                          The only requirement for this type
                                                                 BRIDGE   flowmeter is that the fluid should be
                                                                          very clean (e.g., bottled gases),
                                                                          since the design makes these units
                                                                          very sensitive to dirt particles. For
                                                                          flows with any particulates present,
                                                                          the immersed probe style mass
                                                                          flowmeter should be considered.
                                                                          Immersion Probe Style
                                                                          These units consist of a thermal
                                                                          mass flow probe and integral
                                                                          electronics for a linearized analog
                                                                          output (usually 0 to 5 Vdc, or
                                                                          4 to 20 mA). The probe itself consists
                                               SENSOR                     of two temperature-sensitive RTD
                                                                          (resistance temperature detector
                                                                          sensors). Both are constructed of
      SENSOR                                                              reference grade platinum, coated
                                                                          with glass. These sensors are large,
                                                                          rugged, insensitive to dirt, and easily
Figure 4: Wheatstone bridge circuit of immersion style flowmeters         cleaned. The first sensor constantly
       FMA-78P4 readout/power supply electronics, $1844, and
       FMA-78C10, 3 m (10') interconnecting cable sold separately,
       $89, not shown. See page D-33, D-34 and D-37 for information.
                                                                                       FMA-760A, $1406,                          D
                                                                                       see page D-33 for information.
                                             Both shown smaller than actual size.

                                  Figure 5: Non-symmetrical and symmetrical flow profiles

measures the ambient temperature            (Fig. 4 shown on page D-7). The
of the gas flow and maintains the           output signal of the sensor is the         cubic feet per minute, refer to the
operational temperature differential        bridge voltage (or current) required       equation for converting from actual
of the second sensor. If the                to maintain the constant                   to standardized flow rate.
temperature of the flow varies, the         temperature differential, which is         FMA Series air velocity transducers
first sensor detects and references         non-linearly proportional to the           measure the air mass velocity at the
it, providing a temperature-                mass velocity (r)V. The non-linear         location of the flow sensor. The
compensated basis for                       output of the bridge circuit is then       point of measurement can be critical
measurement.                                linearized and converted to a              if flows are not uniform or flat. If a
The second sensor is the flow               standard analog output signal by           duct does not have a uniform flow,
detection sensor, and is heated to a        the integrally mounted electronics.        point measurements will not be the
temperature 16°C (60°F) higher                                                         same throughout (see Fig. 5). Flow
than the first. As the gas flows past,
                                            Special Consideration                      in a straight duct or pipe will usually
a certain amount of heat is                 for Insertion Probes                       be symmetrical and relatively
transferred from the heated sensor          OMEGA® FMA Series air velocity             uniform if the ratio of straight pipe
to the gas. The heat transfer rate is       transducers measure air mass               length to pipe diameter is at least
proportional to the mass velocity of        velocity. Mass velocity is velocity        10 to 1 and the duct walls are
the gas, or (r)V. It is this principle of   weighed by the gas density (r)V.           relatively smooth. For example,
heat transfer from the sensor to the        The fundamental units of r(V) are          10 diameters in a 152.4 mm (6")
gas that is the key to the immersion-       Ib-m/ft3 x ft/min, or lb-m/ft2/min, but,   diameter pipe is 1524 mm (60").
style probe. When the flow of gas           normally, r(V) is referred to in terms     Tees, elbows, valves and other flow
passing over the flow sensor                of standard feet per minute (SFPM),        obstructions will cause irregularities
increases, the sensor loses more            where the standard reference               in the flow until they have a
heat to the gas. As it loses heat,          conditions are 25°C (77°F) and             sufficient length of straight pipe to
more current is needed to maintain          1 atmosphere pressure. To convert          become more uniform. If a straight
the 16°C (60°F) temperature                 from SFPM to standard cubic feet           section of duct greater than 10
differential between the two                per minute (SCFM), multiply the            diameters in length is unavailable,
sensors. The two sensors operate            standard velocity in SFPM by the           other approaches may be employed
together as part of a Wheatstone            cross sectional pipe area. To              as outlined in the instruction manual
forced null bridge circuit                  convert from SCFM to actual                provided with the unit.
One Omega Drive | Stamford, CT 06907 | 1-888-TC-OMEGA (1-888-826-6342) |                
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