Question

A viscous fluid is flowing through two horizontal pipes. the pressure difference p2 - p1 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 Qb in the longer pipe compare with the rate Qa in the shorter pipe? (A) Qb is the same as Qa (B) Qb is twice as large as Qa (C) Qb is four times as large as Qa (D) Qb is one half as large as Qa (E) Qb is one fourth as large as Qa

Answer 1

Qb is one-half as large as Qa. 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.