Alicat VC Series Volumetric Flow Controller - Manual (Page 27)

27
Operating Principle
All M and V Series Gas Flow Meters (and MC and VC Series Gas Flow Controllers) are based on the
accurate measurement of volumetric flow. The volumetric flow rate is determined by creating a pressure
drop across a unique internal restriction, known as a Laminar Flow Element (LFE), and measuring
differential pressure across it. The restriction is designed so that the gas molecules are forced to move
in parallel paths along the entire length of the passage; hence laminar (streamline) flow is established
for the entire range of operation of the device. Unlike other flow measuring devices, in laminar flow
meters the relationship between pressure drop and flow is linear. The underlying principle of operation
of the 16 Series flow meters is known as the Poiseuille Equation:
Q = ( P
1
-P
2
)�r 4 /8ηL (Equation 1)
Where: Q = Volumetric Flow Rate
P
1
= Static pressure at the inlet
P
2
= Static pressure at the outlet
r = Radius of the restriction
η = (eta) absolute viscosity of the fluid
L = Length of the restriction
Since �, r and L are constant; Equation 1 can be rewritten as:
Q = K (∆P/η) (Equation 2)
Where K is a constant factor determined by the geometry of the restriction. Equation 2 shows the linear
relationship between volumetric flow rate (Q) differential pressure (∆P) and absolute viscosity (η) in a
simpler form.
Gas Viscosity: In order to get an accurate volumetric flow rate, the gas being measured must be
selected (see Gas Select Mode, page 14). This is important because the device calculates the flow rate
based on the viscosity of the gas at the measured temperature. If the gas being measured is not what
is selected, an incorrect value for the viscosity of the gas will be used in the calculation of flow, and the
resulting output will be inaccurate in direct proportion to the difference in the two gases viscosities.
Gas viscosity, and thus gas composition, can be very important to the accuracy of the meter. Anything
that has an effect on the gas viscosity (e.g. water vapor, odorant additives, etc.) will have a direct
proportional effect on the accuracy. Selecting methane and measuring natural gas for instance, will
result in a fairly decent reading, but it is not highly accurate (errors are typically < 0.6%) because
natural gas contains small and varying amounts of other gases such as butane and propane that result
in a viscosity that is somewhat different than pure methane.
Absolute viscosity changes very little with pressure (within the operating ranges of these meters) therefore
a true volumetric reading does not require a correction for pressure. Changes in gas temperature do
affect viscosity. For this reason, the M and V Series internally compensate for this change.