Two horizontal pipes are the same length, but pipe B has twice the diameter of 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 A is $Q = \frac { \Delta V } { \Delta t }$ what is the flow rate in pipe B ?
A) 4 Q
B) 8 Q
C) $Q \sqrt { 2 }$
D) 16 Q
E) 2 Q

Question

Two horizontal pipes are the same length, but pipe B has twice the diameter of 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  A  is  $Q = \frac { \Delta V } { \Delta t }$  what is the flow rate in pipe  B  ?
A)  4 Q 
B)  8 Q 
C) $Q \sqrt { 2 }$
D)  16 Q 
E)  2 Q

Quizplus · Accepted Answer

The flow rate in a pipe is proportional to the fourth power of the diameter (Poiseuille's law). Since pipe B has twice the diameter of pipe A, the flow rate in pipe B is $2^4 = 16$ times that of pipe A.

Two Horizontal Pipes Are the Same Length, but Pipe B Q=ΔVΔtQ = \frac { \Delta V } { \Delta t }Q=ΔtΔV​

Two Horizontal Pipes Are the Same Length, but Pipe B $Q = \frac { \Delta V } { \Delta t }$