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A flow control loop
consisting of a flowmeter, controller, and control valve is used to
control the flow of a gas to a process. Measurements from a pressure
transmitter installed some time ago indicate the incoming air pressure
is typically two bar, but it can vary from one to 2.5 bar due to
process upsets that occur upstream. How will these pressure variations
affect the flow measurement, assuming the flowmeter is calibrated to
operate at a typical pressure of two bar?
Commentary
First, it is the
absolute pressure of the gas that is important when measuring flow. The
pressure of a standard atmosphere is 1.01325 bar absolute, but to make
the mathematics simpler here, we will approximate an atmosphere to be
one bar absolute. Making this approximation, the typical operating
pressure is three bar absolute with variations that can reach from two
to 3.5 bar absolute.
Second, many gas
flow measurements are inferential mass measurements in units expressed
as a standard cubic volume per unit time. However, regardless of the
gas pressure, raw measurements reflect the mass, volume, velocity, or
velocity head of the gas.
With regard to how
these pressure variations affect the flow measurement — it depends. If
the flowmeter measures mass flow, there will (in theory) be no impact
on the flow measurement. That is, a mass flowmeter should not be
affected by pressure variations.
However, if the
flowmeter measures volume or velocity, the effects are inversely
proportional to the variation in absolute pressure. For example, if the
gas were operating at a pressure of 3.5 bar absolute, its volume would
be approximately 3/3.5, or 85.7 percent, of what it would be if the
operating pressure were three bar absolute. As a result, the flowmeter
would measure approximately 14.3 percent lower than it would if the
same mass of gas were flowing at three bar absolute.
The output of
flowmeters that infer mass flow by measuring the differential pressure
across a restriction, such as an orifice plate, Venturi, flow nozzle,
and the like, is also inversely affected by variations in operating
pressure. However, the relationship is not one-to-one, as in the case
of flowmeters that measure volume or velocity, but rather approximately
0.5-to-one. In the above example, the effect of operating at 3.5 bar
absolute is approximately 0.5*14.3, or 7.2 percent. A more accurate
approximation can be calculated as one-sqrt. (3/3.5), or 7.4 percent.
Additional Complicating Factors
Not only is the
flow measurement affected by the type of flowmeter used, but also by
pressure on the raw flow measurement. For example, varying the static
operating pressure on a differential pressure transmitter can cause a
calibration shift of as much as 0.01 percent of the upper range limit
(URL) of the transmitter per bar. This may not seem like much, but
let’s assume the transmitter is not zeroed at operating pressure, its
set span is 50 percent of URL, and the differential pressure is 10
percent of the set span. At a pressure of 3.5 bar absolute, the effect
could be as much as approximately (3.5-1)*0.01/(0.5*0.1), or 0.5
percent of the differential pressure measurement. The effect of this
shift on the flow measurement will be approximately 1.6 percent of
flowrate after taking the square-root relationship of the flowmeter
into account.
About the Author
David W. Spitzer, P.E., is a regular contributor to Flow Control.
Mr. Spitzer is currently a principal in Spitzer and Boyes LLC, offering
engineering, product development, marketing, and distribution
consulting for manufacturing and automation companies. He can be
reached at 845 623-1830.
For More Information: www.spitzerandboyes.com
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