First slide

Viscosity

Question

Two capillary tubes of lengths in the ratio 2:1 and radii in the ratio 1:2 are connected in series. Assume the flow of the liquid through the tube is steady. Then, the ratio of pressure difference across the tubes is

Easy

A

1:8
B

1:16
C

32:1
D

1:1

Solution

$\large l_1:l_2=2:1;\;r_1:r_2=1:2;\;P\propto \frac {l}{r^4}$
$\large \frac {P_1}{P_2}=\frac {l_1}{l_2}\times \left ( \frac {r_2}{r_1} \right )^4\Rightarrow \frac 21\times \left ( \frac 21 \right )^4=\frac 21\times \frac {16}1=\frac {32}{1}$

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