MCAT Physics Question 49: Answer and Explanation
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Question: 49
4. Water flows from a pipe of diameter 0.15 m into one of diameter 0.2 m. If the speed in the 0.15 m pipe is, what is the speed in the 0.2 m pipe?
- A.
- B.
- C.
- D.
Correct Answer: B
Explanation:
It is known that water flows faster through a narrower pipe. The speed is inversely proportional to the cross-sectional area of the pipe because the same volume of water must pass by each point at each time interval. Let A be the 0.15 m pipe and B the 0.20 m pipe, and use the continuity equation:
νAAA = νBAB
where ν is the speed and A is the cross-sectional area of the pipe. Because ν is inversely proportional to the cross-sectional area, and the area is proportional to the square of the diameter
we obtain the following:
Choice (B) most closely matches our result and is thus the correct answer.