Answer to Question #111430 in Physics for John Guz

Question

You can drain a tank of viscous fluid through your favorite hose in exactly 10 minutes.

Sadly you lose your favorite hose and must use a spare hose which has twice the length and a diameter which is 12% less than your favorite hose.

How long does it take to drain the tank with the spare hose under otherwise identical conditions? (to 2 s.f and in minutes)

Answer 1

$$\frac{\Delta V}{\Delta t}=\frac{\pi d^4\Delta p}{128\eta l}$$

$$\frac{\Delta t'}{\Delta t}=\frac{ d^4l'}{d'^4 l}$$

$$\frac{\Delta t'}{10}=\frac{ 2}{(1-0.12)^4 }$$

$$\Delta t'=33\ min$$