Energy& Poiseuille's law

[SaintJude]

Can someone explain the answer of this question? This is from the MCAT test makers.
Boiler scale" is the deposit of buildup inside a pipe as time goes on--(thanks ljc)

View attachment Picture 5 jpeg.jpg

Highlight here for answer: D.

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[ljc]

"Boiler scale" is the deposit of buildup inside a pipe as time goes on (I had to look this up).
This means radius is decreasing. As radius decreases, we see a decrease in flow rate. In order to increase flow rate, you must increase the velocity of the liquid, and thus increase pressure (which means increased energy). This means A is out.

We can also see that the relationship is probably not linear (because r is raised to the 4th power). So B is out.

This leaves C and D. C implies that eventually you would reach a point where no matter how small your pipe gets, you won't need to put in any additional energy to pump the same volume. This doesn't make sense, so the answer must be D.

 

[MedChad]

I have never seen this relationship graphed before from Poiseuilles law. What I have seen was a positive linear relationship between linear pressure and flow
an exponential growth between r^4 and flow
and finally an inverse relationship with L or n v.s flow.

I would also think choice D since it says our solution is at high temperature, meaning high energy, and D is the only graph that is curved toward energy ( the greater change between the two). But I am only about 80% sure on this one. Any other suggestions?

 

[MedPR]

"Boiler scale" is the deposit of buildup inside a pipe as time goes on (I had to look this up).
This means radius is decreasing. As radius decreases, we see a decrease in flow rate. In order to increase flow rate, you must increase the velocity of the liquid, and thus increase pressure (which means increased energy). This means A is out.

We can also see that the relationship is probably not linear (because r is raised to the 4th power). So B is out.

This leaves C and D. C implies that eventually you would reach a point where no matter how small your pipe gets, you won't need to put in any additional energy to pump the same volume. This doesn't make sense, so the answer must be D.

Yea, you have to know what a boiler scale is (I didn't) to answer this question. Initially I thought the question was getting at the fact that viscosity decreases as temperature increases, so it would be an inverse relationship since Q is proportional to 1/viscosity.

If you know what a boiler scale is, this question should be simple.

If you double r you increase the flow by 16, but if you decrease the flow by a factor of 1/16. The relationship between r and flow (Q) is an exponential one, so A and B are out.

C implies that over time, the shrinking radius stops affecting the required energy. This doesn't make sense.

D is right. D is right because as time increases, radius decreases (again, this requires you to know what a boiler scale is). As the radius decreases, the energy required to push fluid through the pipe increases exponentially and increases to infinity.

TBR has a shortcut that goes something like this. Curved graphs will bend towards the axis that is most affected by change. I'm not sure I really understand this shortcut, but I guess in this case it shows that the energy required to maintain Q is affected more than the time..? I don't know. Just ignore that if you don't understand it. It's not necessary.

 

[SaintJude]

Alright, this makes sense. Well I actually got this question from the "2015 Preview Guide" which includes a few questions on some old,usual MCAT topics..in case some haven't had a chance to look at it.

I think what threw me of was seeing P's law related in terms of energy, but all your explanations make sense. Thanks.

 

[MedPR]

Alright, this makes sense. Well I actually got this question from the "2015 Preview Guide" which includes a few questions on some old,usual MCAT topics..in case some haven't had a chance to look at it.

I think what threw me of was seeing P's law related in terms of energy, but all your explanations make sense. Thanks.

Yea, remember that Q is flow rate, which implies a velocity of some sort. Therefore KE is involved as well.

 

[MT Headed]

I'm probably reading too much into the question, but there is an underlying assumption that the scale builds up at a constant rate, I.e. R=R0-(bt). It is conceivable that the scale does not build up at a constant rate, but rather builds up quickly at first and more slowly later (due to increased turbulence?) and therefore answer B is possible.

But i'm probably thinking about this too hard.

 

[theseeker4]

I'm probably reading too much into the question, but there is an underlying assumption that the scale builds up at a constant rate, I.e. R=R0-(bt). It is conceivable that the scale does not build up at a constant rate, but rather builds up quickly at first and more slowly later (due to increased turbulence?) and therefore answer B is possible.

But i'm probably thinking about this too hard.

Yeah, I would stick with the more obvious solution, which would be D, instead of searching for the conditions which could allow a different answer.

 

[SaintJude]

Wanted to just quickly resurrect this thread b/c someone just posted a thread about pressure in the capillaries (summary: Greatest BP drop is in arterioles and lowest BP in capillaries)

Would D also be the energy graph for a blood vessel w/ atherosclerosis ?

 

[EnginrTheFuture]

Interesting point.... if the artherosclerosis was getting worse (smaller and smaller radius) yep!

Just a note: I'm pretty sure that is graphing energy used, not energy needed/time (power). If they wanted to graph how the power was changing I don't see why they would label the axis "energy"

The rate at which the energy is consumed increases as time goes on, thus the energy used is a power relationship as seen in D. The power vs energy relationship would be the derivative of that graph which I don't think we can deduce.