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Name: Kris
Status: Other
Grade: 9-12
Location: NY
Country: United States
Date: Spring 2010


Question:
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?



Replies:
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:

http://www.engineeringtoolbox.com/minor-pressure-loss-ducts-pipes-d_624.html

but any good chemical engineering text should discuss this.

Hope this helps,
Burr Zimmerman


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.

Vince Calder



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