EK Physics #576 - Flow Rate

[ilovemcat]

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Question 576: An ideal fluid flows through a pipe. If the length of the pipe is doubled while the radius is decreased by a factor of 2, the volume of fluid passing any point in a given second will:

A. decrease by a factor of 4
B. decrease by a factor of 2
C. remain the same
D. increase by a factor of 4

 

[ilovemcat]

The answer was C.

I thought the answer was B. The way I reasoned this problem was by realizing that Flow Rate = Area x Velocity OR Volume / Time.

Using the later equation, I figured that decreasing the radius would decrease the area by a factor of 4. Multiplying that (1/4) times an increase in length by a factor of two (2), I assumed that the flow rate would cut in half.

The explanation EK gives explains that, "For an ideal fluid the flow rate is independent of the length of the pipe. An ideal fluid obeys the continuity equation Q = Av. Since A = pi r^2, doubling r will increase A by a factor of four which will reduce v by a factor of four."

They have their explanation backwards. Radius is halved so Area would decrease by a factor of 4 and velocity would increase by a factor of 4. But anyways, was I wrong to approach the problem the way I did above? I'm having a hard time understanding how flow rate is independent of length.

 

[ilovemcat]

The answer was C.

I thought the answer was B. The way I reasoned this problem was by realizing that Flow Rate = Area x Velocity OR Volume / Time.

Using the later equation, I figured that decreasing the radius would decrease the area by a factor of 4. Multiplying that (1/4) times an increase in length by a factor of two (2), I assumed that the flow rate would cut in half.

The explanation EK gives explains that, "For an ideal fluid the flow rate is independent of the length of the pipe. An ideal fluid obeys the continuity equation Q = Av. Since A = pi r^2, doubling r will increase A by a factor of four which will reduce v by a factor of four."

They have their explanation backwards. Radius is halved so Area would decrease by a factor of 4 and velocity would increase by a factor of 4. But anyways, was I wrong to approach the problem the way I did above? I'm having a hard time understanding how flow rate is independent of length.

Ah, I see what I did. I confused distance traveled for length of the whole pipe. Flow rate doesn't change. But if Area decreases by a factor of 4, velocity (distance / time) would increase by a factor of 4 in order to keep the flow rate constant. Distance traveled is independent of the length of the pipe.

 

[Rabolisk]

It only makes sense that length would not change the flow rate. Would water travel faster because it had to travel longer??

You probably confused this with the resistance of a resistor, which does vary with the length of a resistor.

 

[shffl]

This question would've confused me since it asked for volume. But I assume to get the volume we just have to get flow rate?

 

[Rabolisk]

T asked for volume per second, which is the definition of flow rate.

 

[shffl]

T asked for volume per second, which is the definition of flow rate.

woops i didnt finish reading the question 🙄

 

[DingDongD]

Isn't it A? How can it be C? Sorry for bringing an old thread to life. That's the only one with it decreasing by 4, unless I did not follow your argument correctly.

 

[aldol16]

All of these answer choices violate Pouseille's law...

 

[David513]

It's C because Q=A*v a.k.a. volume of fluid passing a given point in a second=area of the pipe * velocity of the fluid in m/s
If you decrease the area by a factor of 4 by decreasing the radius by a factor of 2, the velocity of the fluid will increase as a result by an equal factor (4). (You have higher uniform translational motion/decreased pressure.) Therefore, the change in v compensates for the change in A and you remain with the same Q. Hence choice C.