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)2Q
B)4Q
C)8Q
D)16Q
E)Q $\sqrt { 2 }$

Question

Quizplus · Accepted Answer

The flow rate in a pipe under viscous flow is given by the Hagen-Poiseuille equation: $Q = \frac{\pi \Delta P r^4}{8 \eta L}$. Since the diameter of pipe B is twice that of pipe A, the radius of pipe B is also twice that of pipe A. Therefore, the flow rate in pipe B is $2^4 = 16$ times the flow rate in pipe A, making it 16Q.

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

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