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 = , what is the flow rate in pipe B?

Answer 1

Answer:

flow rate in pipe B is 16 times the flow in pipe A

Explanation:

According to the poiseuille's law, flow rate  is is given as

$Q = \frac{ \pi Pr^{4}}{8\eta*L}$

Flow rate  in the pipe will remain same as above i.e,

$Q_{A} = \frac{\pi Pr^{4}}{8\eta*L}$

Flow in the pipe be will be

As diameter OF PIPE B is doubled

AND length of both pipes remained same

$Q_{B} = \frac{\pi P(2r)^{4}}{8\eta*L}$

          $= \frac {16\pi P(r)^{4}} {8\eta*L}}$

          so we have

flow rate in pipe B is 16 times the flow rate  in pipe A