Two horizontal pipes have the same diameter, but pipe B is twice as long as pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe B is Q = $\frac { \Delta V } { \Delta t }$ what is the flow rate in pipe A?
A)2Q
B)4Q
C)8Q
D)16Q
E)Q $\sqrt { 2 }$

Question

Quizplus · Accepted Answer

According to the Hagen-Poiseuille equation for viscous flow, the flow rate is inversely proportional to the length of the pipe. Since pipe B is twice as long as pipe A, the flow rate in pipe A will be twice that in pipe B, hence 2Q.

Two Horizontal Pipes Have the Same Diameter, but Pipe B ΔVΔt\frac { \Delta V } { \Delta t }ΔtΔV​

Two Horizontal Pipes Have the Same Diameter, but Pipe B $\frac { \Delta V } { \Delta t }$