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Pressure question
cathy4208
#1 Posted : Monday, June 29, 2015 2:19:01 AM
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When comparing two points of fluid flowing through the same horizontal pipe, if the fluid velocity is greater, then:
A) The temperature is less
B) The temperature is greater
C) The temperature is unchanged
D) The pressure is greater

I'm not sure how to approach the question; please advise what the relationship between temperature and velocity is.
joelhutchinson
#2 Posted : Tuesday, June 30, 2015 12:58:16 AM
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Could you please list the question number and where you found it?
joelhutchinson
#3 Posted : Tuesday, June 30, 2015 3:20:45 AM
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Hi there,

So unfortunately, this is a very ambiguous question. In general, the relationship between temperature and velocity in a fluid is quite complicated, however we can think about the reasoning that the question maker was after.

First of all, there's nothing to indicate that this is a non-ideal fluid, so we can safely apply Bernoulli's equation. Since it's a horizontal pipe, the heights at the two points are the same, so that means if the velocity is greater at one point, then the pressure must be less there (this is the same reasoning behind lift forces on an airplane wing).

Now, recall that pressure is due to the impulse exerted on the walls by the individual molecules in the course of their random translational motion. Less pressure means less random motion which is what we associate with the temperature of a substance. Thus, we should expect a lower temperature (i.e. answer A).

You can also get this relationship from the ideal gas law (of course there's nothing suggesting this fluid is a gas):
PV=nRT,
which says that pressure is proportional to temperature (at fixed volume).

Hope this helps.
cathy4208
#4 Posted : Wednesday, July 01, 2015 12:00:16 AM
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Hi there,

Thanks! That helps to clarify! It was EK 1001, #569.
My original thought was that if there was an increase in velocity, then because KE = 3/2RT, then there would be an increase in temperature. Can you point me along why this train of thought is wrong? Thanks in advance!
heatherjudd
#5 Posted : Tuesday, July 07, 2015 5:22:42 PM
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Hey Cathy,
There is a difference between uniform translational velocity (lets call this our regular velocity) and random translational velocity (this is the random molecule movement). Uniform is when the wind blows, whereas random is the temperature of the air as it does so. There can be both hot and cold winds, and both of them will have less pressure than stagnant air.
You don't need to know much about temperature/pressue, except that temperature means molecules move more slowly and hence they aren't hitting each other or the surface of the container as hard so they excert less force per area (less pressure). If you want to confirm this for yourself, try blowing up a balloon and putting it in the fridge overnight - it will shrink!
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