fluid flow and temperature

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This question came from the EK Physics 1001, question #569.

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 put down D, but the answer is A. It makes sense that greater pressure causes greater velocity, especially when the area decreases, as I think that is what is happening (but I am obviously wrong) and I don't get how lowering the temperature can cause a increase in velocity...am I approaching this problem incorrectly or is there some other concept that I am missing? 😕

EK explains that from KE=(3/2)RT, where KE is the kinetic energy due to random translational motion of molecules and not their uniform velocity, we can conclude that the temperature is decreased when fluid velocity increases. But if temperature is decreased then wouldn't KE decrease as well? And I thought random translational motion doesn't contribute to overall velocity....
 
This question came from the EK Physics 1001, question #569.

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 put down D, but the answer is A. It makes sense that greater pressure causes greater velocity, especially when the area decreases, as I think that is what is happening (but I am obviously wrong) and I don't get how lowering the temperature can cause a increase in velocity...am I approaching this problem incorrectly or is there some other concept that I am missing? 😕

EK explains that from KE=(3/2)RT, where KE is the kinetic energy due to random translational motion of molecules and not their uniform velocity, we can conclude that the temperature is decreased when fluid velocity increases. But if temperature is decreased then wouldn't KE decrease as well? And I thought random translational motion doesn't contribute to overall velocity....

It is my opinion that this question cannot be answered, due to its ambiguity. So do not be so quick to give up on your thought process and answer, because an argument can be made in support of choice D. An argument can also be made to support choice B.

Let's assume a few things that it seems the question writer visualized. The radius of the pipe is constant, the fluid is ideal and noncompressible, and as an ideal fluid flows through a uniform pipe, the pressure gradient is also uniform. The thing the writer is assuming that I believe is not a good assumption is that the fluid behaves like an ideal gas. Is there more to the question that tells you it's an ideal gas?

As metioned by the previous poster, the KE = 3/2 RT equation descibes an ideal monatomic gas. While gases are fluids, nowhere in the question did is state that the fluid in question is an ideal monatomic gas. It could be a liquid.

The real question as I see it is the impact of temperature on the viscosity on the fluid and the impact of fluid temperature on the pressure differential from one end of the pipe to the other. To determine the impact of viscosity, it is important that we know whether the fluid is a liquid or a gas.

If we assume the fluid to be a liquid, then the explanation they present no longer holds. It would be more important to consider the impact of temperature on the viscosity of the liquid. You are right to assume that as temperature goes up, the average velocity should increase, because of reduced viscosity in the liquid (generally true).

On the other hand, if temperature increases too much, the random motion can lead to nonideal behavior which creates drag, and could potentially result in a slower fluid speed (when the Reynolds value is high enough that the flow becomes turbulent). So, without any information, we can't really decide.

The greater speed could be due to many factors, so treat this as a learning experience rather than a test question.

In the matter of a few paragraphs, we have looked at several factors, all of which are open to interpretation because of the ambiguity in this question.

So on this particular question, here is what you should probably do. Understand their explanation and support of choice A if the fluid is an ideal gas (although to be honest, I disagree with their explanation). But also be able to support why you feel choice D is best. Consider why choice B could also be correct. You are using the material to review, so make the most out of the question. And realize that the MCAT questions will be more infromation-laden, because they have a passage full of information behind them. By knowing what could make choice A , choice B, or choice D correct, you'll be better equipped to extract what you need from the passage, should something like this every pop up.

Good luck studying!
 
Thanks for clarifying this misleading question, and I had a feeling that this was somewhat ambiguous to begin with because I also just assumed that it is a liquid...
 
Although berk has given you an in depth explanation on some of the issues with this question, I think this is a perfect question to exemplify why its important to always ask yourself what the test maker is trying to test. In this case, at soon as I saw "same horizontal pipe" and "two points of fluid flow", I immediately jumped to: "This question is going to test me on whether I understand bernoulli's principle of near-ideal fluid flow and the relationship between fluid velocity and fluid pressure."

So while it's true that the question doesn't seem to indicate that the fluid flow is near-ideal, because of the wording of the questions and my instinct about what concept is trying to be tested in this question, I'm pretty sure that it was intended to be near-ideal. They should have included that though...
Caveat: This question does not work with completely ideal fluid flow. If you can figure out why, you really understand what's going on, and I'll give you a prize lol.

Now, given that fluid flow in this problem is near-ideal, we can use bernoulli's principle. Bernoulli's principle states something to the effect of, "Fluid velocity and fluid pressure are inversely related. That is, when the fluid velocity of an ideal fluid increases, the fluid pressure decreases. When the fluid velocity of an ideal fluid decreases, the pressure must increase."
It might seem counter-intuitive, but this is actually what happens in ideal systems. For instance, if you have a pipe demarcated by points "A" "B" and "C", and there is an instantaneous decrease in the pipe raidus at point B, then you'll have a lower fluid velocity and higher fluid pressure in the compartment from A to B (larger cross-sec area), and a higher fluid velocity and a lower fluid pressure in the compartment from B to C (smaller cross-sec area). Again, counterintuitive, but it's true. Check out the picture on wikipedia to see a real-example of this: http://en.wikipedia.org/wiki/Bernoilli_equation.

What the question is really asking is: "If I increase the velocity of an ideal fluid, then what happens to the pressure? Then, knowing how pressure and temperature are related, what happens to the temperature?"

See the trick? The question wants you to realize that you are to apply bernoulli's principle, and the extend that application to include temperature. <= This relates to why the question must be dealing with a "near ideal" fluid and not an "ideal" fluid.

So let's work through it:

If the fluid velocity increases, then bernoulli's principle says that the fluid pressure must decrease. Okay, so pressure goes down. Now, what does this say about the temperature? Well pressure and temperature are related in that if pressure decreases, then temperature also decreases.

So just knowing those facts, you can work out that the answer should be "A".

Now, let's talk about kinetic energy as it seems that there is a bit of confusion on that point.

When we are talking about "average kinetic energy" of the particles, meaning the kinetic energy that determines the temperature, it is implied in this definition that the kinetic energy we are talking about is that energy which contributes to the random motion of the particles such that they collide with each other and release heat. So a higher kinetic energy = a higher frequency of collisions = higher temperature.

In this problem, however, in addition to that "kinetic energy of collisions" we also have a more or less uniform motion of fluid flow which carries with it another kinetic energy; that kinetic energy's velocity, because it's in one uniform direction, does not contribute to the temperature, because it does not increase the frequency of collisions. Only the kinetic energy that causes collisions will increase the temperature. This is why a faster fluid flow cannot increase temperature, unless, as berk review stated, it also increases turbulent flow, thereby increasing the temperature.

In a "near-ideal" fluid which I've set up here, this is the crux of the issue that Berk is talking about:
Which has a greater effect on temperature in a near-ideal fluid system: the increase in turbulent flow and resultant collisions due to increased forward fluid flow, or the decrease in pressure brought about by the application of bernoulli's principle. Obviously for this problem to work, I've had to implicitly define a "near-ideal fluid" to mean one where the contributions from turbulent flow to temperature are less than those from the application of bernoulli's principle. These two concepts really are at odds because bernoulli's principle can't even be applied to fluid systems with a high enough mach number (basically meaning non-ideal fluids)...but for the sake of appeasing the test maker and what he's trying to test, just play along and assume that the fluid is ideal enough to follow bernoulli's principle, but also just turbulent enough to have collisions leading to temperature changes. Is it a bad compromise? Yes...but I wouldn't be surprised if a problem like this slipped past the AAMC error checkers. :/
 
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Caveat: This question does not work with completely ideal fluid flow. If you can figure out why...

This question is quite ambiguous but it has definitely sparked a terrific discussion by you guys. I think it can't relate to completely ideal flow because the assumptions that we used to allow us to use the basic form of Bernoulli's equation (which helps us to easily arrive at the relationship between pressure and velocity) presuppose that the fluid is an ideal-flowing liquid (incompressible, inviscid)...but then we're forced to put that aside and apply ideal gas laws to get a relationship between temperature and pressure changes (which is really quite anti-Bernoulli and contrary to our earlier assumptions).

There really is some terrific stuff in the two pervious posts. Did you guys both get 15s on the PS section? 🙂
 
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Thanks Vihsadas for the thorough explanation, I wouldn't have come up with the correct answer without it and now I actually understand the depth of the question, despite any ambiguities.
 
Although berk has given you an in depth explanation on some of the issues with this question, I think this is a perfect question to exemplify why its important to always ask yourself what the test maker is trying to test. In this case, at soon as I saw "same horizontal pipe" and "two points of fluid flow", I immediately jumped to: "This question is going to test me on whether I understand bernoulli's principle of near-ideal fluid flow and the relationship between fluid velocity and fluid pressure."

So while it's true that the question doesn't seem to indicate that the fluid flow is near-ideal, because of the wording of the questions and my instinct about what concept is trying to be tested in this question, I'm pretty sure that it was intended to be near-ideal. They should have included that though...
Caveat: This question does not work with completely ideal fluid flow. If you can figure out why, you really understand what's going on, and I'll give you a prize lol.

Now, given that fluid flow in this problem is near-ideal, we can use bernoulli's principle. Bernoulli's principle states something to the effect of, "Fluid velocity and fluid pressure are inversely related. That is, when the fluid velocity of an ideal fluid increases, the fluid pressure decreases. When the fluid velocity of an ideal fluid decreases, the pressure must increase."
It might seem counter-intuitive, but this is actually what happens in ideal systems. For instance, if you have a pipe demarcated by points "A" "B" and "C", and there is an instantaneous decrease in the pipe raidus at point B, then you'll have a lower fluid velocity and higher fluid pressure in the compartment from A to B (larger cross-sec area), and a higher fluid velocity and a lower fluid pressure in the compartment from B to C (smaller cross-sec area). Again, counterintuitive, but it's true. Check out the picture on wikipedia to see a real-example of this: http://en.wikipedia.org/wiki/Bernoilli_equation.

What the question is really asking is: "If I increase the velocity of an ideal fluid, then what happens to the pressure? Then, knowing how pressure and temperature are related, what happens to the temperature?"

See the trick? The question wants you to realize that you are to apply bernoulli's principle, and the extend that application to include temperature. <= This relates to why the question must be dealing with a "near ideal" fluid and not an "ideal" fluid.

So let's work through it:

If the fluid velocity increases, then bernoulli's principle says that the fluid pressure must decrease. Okay, so pressure goes down. Now, what does this say about the temperature? Well pressure and temperature are related in that if pressure decreases, then temperature also decreases.

So just knowing those facts, you can work out that the answer should be "A".

Now, let's talk about kinetic energy as it seems that there is a bit of confusion on that point.

When we are talking about "average kinetic energy" of the particles, meaning the kinetic energy that determines the temperature, it is implied in this definition that the kinetic energy we are talking about is that energy which contributes to the random motion of the particles such that they collide with each other and release heat. So a higher kinetic energy = a higher frequency of collisions = higher temperature.

In this problem, however, in addition to that "kinetic energy of collisions" we also have a more or less uniform motion of fluid flow which carries with it another kinetic energy; that kinetic energy's velocity, because it's in one uniform direction, does not contribute to the temperature, because it does not increase the frequency of collisions. Only the kinetic energy that causes collisions will increase the temperature. This is why a faster fluid flow cannot increase temperature, unless, as berk review stated, it also increases turbulent flow, thereby increasing the temperature.

In a "near-ideal" fluid which I've set up here, this is the crux of the issue that Berk is talking about:
Which has a greater effect on temperature in a near-ideal fluid system: the increase in turbulent flow and resultant collisions due to increased forward fluid flow, or the decrease in pressure brought about by the application of bernoulli's principle. Obviously for this problem to work, I've had to implicitly define a "near-ideal fluid" to mean one where the contributions from turbulent flow to temperature are less than those from the application of bernoulli's principle. These two concepts really are at odds because bernoulli's principle can't even be applied to fluid systems with a high enough mach number (basically meaning non-ideal fluids)...but for the sake of appeasing the test maker and what he's trying to test, just play along and assume that the fluid is ideal enough to follow bernoulli's principle, but also just turbulent enough to have collisions leading to temperature changes. Is it a bad compromise? Yes...but I wouldn't be surprised if a problem like this slipped past the AAMC error checkers. :/

Hey! So I definitely get where you're coming from with Bernoulli's equation because this is also how I approached the question, but I thought volume and pressure were directly related, only when moles and pressure remained constant (Charles's Law) and that the speed of a particle was directly proportional to the square root of its temperature? So wouldn't it not be true that pressure and temperature are inversely related?

Thank you for your explanation on KE and velocity! I think this is where the test writer was coming from because the previous question dealt with fluid velocity and random translational motion. The explanation for that question was "Energy of an ideal fluid is conserved as it flows. If the molecules have the same gravitational PE (which they would in a horizontal pipe_ and greater KE due to greater uniform velocity, then they must have less KE due to random translational motion" - which, as you stated, would lead to a decrease in temperature.
 
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