Q: Capillary tubes of lengths l and 2l are connected in series. Their radii are r and 2r respectively. If stream line flow is maintained and pressure difference across first and second capillary tubes are P_{1} and P_{2} respectively, then find the ratio P_{1}/P_{2}

Sol: Equating the rate of flow of liquid

Q_{1} = Q_{2} and $\large Q = \frac{P \pi r^4}{8 \eta l}$

$\large \frac{P_1 \pi r^4}{8 \eta l} = \frac{P_2 \pi (2r)^4}{8 \eta (2l)} $

$\large \frac{P_1}{P_2} = 8 $