Gas Properties in a Pipe
Country: United States
Date: Spring 2010
Consider a pipe with turbulent air flowing through it.
The diameter of the pipe remains constant. Air entering the pipe is
measured to have a velocity V. What are the effects of the pressure
drop due to friction in the pipe? In the every day sense, friction
tends to slow things down. But if the air slows down, then
continuity says that its density has to increase. But how can its
density increase if the pressure is dropping?...I am
confused...Basically, what are the differences in the air's
properties as a result of the friction?
Kris, the density of the air is a function of pressure, you are right.
But it does not slow down as it travels through the pipe. Your
'everyday' sense that friction slows things down is applicable to a
sliding object, but not to gas flow in a pipe.
The complication here is that air is compressible. Since the pressure
is dropping, the volume expands, and the gas accelerates through the
pipe (think of opening up a balloon - the gas accelerates out of the
balloon as you release it). At steady state, even if the mass flow
rate is constant through the pipe, the volume flow rate is not
(necessarily) -- and vice-versa -- because the pressure is changing.
The overall energy of the gas coming out of the pipe is lower, but
some of the potential energy (stored as the pressurized gas) has been
converted to kinetic energy (velocity). Of course, these "minor
losses"* in pipes are small for gases, so if you were to run an
experiment, you would not see huge differences the way you might for
water in a garden hose.
*The pressure drop due to friction, aka viscosity, is known as 'minor
losses'. There are many different correlations for many different pipe
materials, fluids, and flow regimes to estimate minor losses. One
place to start reading is here:
but any good chemical engineering text should discuss this.
Hope this helps,
You raised your own "red flag" -- "a pipe with turbulent air flowing"...
To my knowledge, there is no model for predicting the turbulent flow.
In turbulent flow, the behavior of the behavior depends on time and
position, which in turn affect pressure, density, temperature etc.
Other's more expert than I may have a better answer, but when I see
the words, "turbulent flow" my warning horns go up.
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Update: June 2012