Alicat VC Series Volumetric Flow Controller - Manual (Page 33)

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Volumetric Flow Meters and Controllers Under Pressure
V and VC Series Volumetric Flow Meters/Controllers are intended for use in low pressure
applications. This is because an accurate measurement of the volumetric flow rate by means
of differential pressure requires the flow at the differential pressure sensor to be in a laminar
state. The state of the flow is quantified by what is known as the Reynolds Number. If the
Reynolds Number gets above a certain point, generally accepted as approximately 2000, the
flow will become non-laminar. The Reynolds Number for a given Newtonian fluid flow is defined
as:
Re = ρVL/η
Where: ρ = density
V = average velocity
L = Constant determined by length and geometry of passage
η = absolute viscosity
From this relationship we see that increasing the gas density or velocity increases the Reynolds
Number, and increasing the gas viscosity decreases the Reynolds number. For a given gas in
a given meter at a given temperature, L and η are roughly fixed constants.
For the purpose of illustration, let us put two 100 (S)LPM flow meters, identical in every way
except that one is a volumetric flow meter and one is a mass flow meter, in series with one
another in a pipeline. Now let us pass a small constant air flow through the meters, thus fixing
the velocity V though both meters. With the flow fixed, let us begin increasing the pressure,
and thus the density ρ. The mass flow meter, which is measuring the absolute pressure and
compensating for the density change registers this pressure increase as an increase in mass
flow rate because the number of molecules of gas keeps going up in the fixed volume of flow.
In addition, the Reynolds number has increased proportionately with the pressure increase
because the density goes up with the pressure. If you increase the pressure high enough,
the mass flow meter will max out at 100 SLPM, the Reynolds number has increased fairly
dramatically, and the volumetric meter still registers your small fixed flow rate.
Now if we maintain the higher pressure and try to take the volumetric meter up to its published
full scale flow of 100 LPM, our density ρ AND our velocity V will be high, which often results
in a high Reynolds number and non-laminar flow. When the flow is non-laminar, the Poiseuille
Equation upon which we base our volumetric flow measurement is no longer valid and the
meter reading is therefore no longer valid.
Gas properties also need to be taken into account in deciding whether you can use a volumetric
flow meter at a particular line pressure. Helium, which has a relatively low density and a
relatively high viscosity at standard conditions, can generally get away with higher pressures in
a volumetric flow meter. Propane, on the other hand, has a relatively high density and relatively
low viscosity making it a considerably more difficult gas to measure at higher pressures in a
volumetric flow meter. In air, most volumetric meters make valid full scale measurements up to
10-15 PSIG line pressure.