A viscous fluid is flowing through two horizontal pipes. The pressure difference $P_{2} - P_{1}$ between the ends of each pipe is the same. The pipes have the same radius, although one is twice as long as the other. How does the volume flow rate $Q_{B}$ in the longer pipe compare with the rate $Q_{A}$ in the shorter pipe?

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$Q_{B}$ is the same as $Q_{A}$

$Q_{B}$ is twice as large as $Q_{A}$

$Q_{B}$ is four times as large as $Q_{A}$

$Q_{B}$ is one-half as large as $Q_{A}$

answer is D.

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Detailed Solution

A longer pipe offers a greater resistance to the flow of a viscous fluid than a shorter pipe does. The volume flow rate depends inversely on the length of the pipe. For a given pipe radius and pressure difference between the ends of the pipe, the volume flow rate is less in longer pipes. In this case the longer pipe is twice as long, so its volume flow rate $Q_{B}$ is one-half that of $Q_{A}$ .

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