Three capillary tubes of same radius 1 cm but of lengths 1 m, 2 m and 3 m are fitted horizontally to the bottom…

Q: Three capillary tubes of same radius 1 cm but of lengths 1 m, 2 m and 3 m are fitted horizontally to the bottom of a long vessel containing a liquid at constant pressure and flowing through these. What is the length of a single tube which can replace the three capillaries.

Sol: $\large V = \frac{P \pi r^4}{8 \eta l}$

$\large V \propto \frac{1}{l}$

$\large V = V_1 + V_2 + V_3 $

$\large \frac{1}{l} = \frac{1}{l_1} + \frac{1}{l_2} + \frac{1}{l_3} $

$\large \frac{1}{l} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} $

$\large l = \frac{6}{11} m$