Fluid Question

[SSerenity]

The question is here, form wikipremed:

http://www.wikipremed.com/01physicscards.php?card=334

click 'next' to see the answer.


However, I don't agree with the answer! If we decrease the cross sectional area of the pipe, we will increase the SPEED of the fluid, but the flow rate should remain the same.

What am I missing here?

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[DrknoSDN]

If we decrease the cross sectional area of the pipe, we will increase the SPEED of the fluid, but the flow rate should remain the same.

Did the question change? Because constant flow does not apply here.

It's just saying that if the pipe was only a 1" diameter the volume of the pipe is smaller so it will fill up faster. (Flow rate only remains constant for closed pipe systems with horizontal flow)
Conceptually if you push fluid molecules through a pipe, you know they have to displace the molecules in front of them. That logic does not apply to gravity fluid problems because the fluid is not displacing other fluid. It is flowing into a previously empty space so flow rate due to gravity is not always a constant.

The example is also action packed with issues because there would need to be some "air escape" in the barrel or else the air would need to flow up the pipe against the flow of the fluid.
And the drum bursting implies there is no air escape. But if you ignore that for simplicity... The math is still wrong.

Considering the pipe and drum are empty to begin you need to use the V=root(2gh) equation to determine how fast the fluid is flowing out of the large tank.
http://en.wikipedia.org/wiki/Torricelli's_law

With velocity being constant regardless of pipe diameter then the larger pipe should fill the drum faster. (Unless Drum volume is <<< pipe volume) Then the pipes fill at the same rate.

Extremely flawed question.

 

[Integrated MCAT Course]

You are right DrknoSDN. This question has serious problems. I am sorry for the confusion, SSerenity. The more advanced your appreciation of the issues involved, the more befuddling it becomes. That's the hallmark of a certain kind of flawed MCAT practice question. Did the question writer really mean for it to be about this, or is it a kind of jujitsu, and really about that? An improved version of this question will be available soon in future editions. I really appreciate this kind of thing because it makes WikiPremed better.

The goal for this question is to encourage conceptualization of the fact that pressure varies in a simple way with depth regardless of the shape of the container. I think specifying the pipe as a drip-drain for a condenser will fix the problem.

 

[DrknoSDN]

JohnWetzel, I have new and improved respect for WikiPremed. Some of the best customer service companies in the world do not have response times as fast as what you just demonstrated. Truly admirable.
Also sorry for pasting your images into this thread. Let me know if I should edit them out.

 

[Integrated MCAT Course]

JohnWetzel, I have new and improved respect for WikiPremed. Some of the best customer service companies in the world do not have response times as fast as what you just demonstrated. Truly admirable.
Also sorry for pasting your images into this thread. Let me know if I should edit them out.

Thank you for the kind comment, and please don't worry about posting elements from WikiPremed here on SDN. SDN and WikiPremed both publish under a Creative Commons license. It's fine to post things from WikiPremed here without asking.