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

The flow rate of a fluid through a pipe is directly proportional to the cross-sectional area of the pipe and the pressure difference across the length of the pipe. Therefore, if the diameter and pressure difference are the same in both pipes A and B, the flow rate is proportional to the cross-sectional area, which is equivalent to the product of the diameter and the length of the pipe. Pipe B has twice the length of pipe A, but the same diameter, so its cross-sectional area is twice that of pipe A. As such, the flow rate in pipe B is twice that of pipe A, which is Q. Therefore, the flow rate in pipe A is 2Q.

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

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