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  4. Water is flowing through a tube of non-uniform cross-section. If the radii of the tube at the entrance and exit are in the ratio 3:2 , then the ratio of the velocity of liquid entering and leaving the tube is

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Q. Water is flowing through a tube of non-uniform cross-section. If the radii of the tube at the entrance and exit are in the ratio $3:2$ , then the ratio of the velocity of liquid entering and leaving the tube is

NTA AbhyasNTA Abhyas 2020

Solution:

Using equation of continuity
$A_{1}v_{1}=A_{2}v_{2} \, \Rightarrow \pi r_{1}^{2}v_{1}=\pi r_{2}^{2}v_{2}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\frac{r_{2}^{2}}{r_{1}^{2}}=\left(\frac{2}{3}\right)^{2}=\frac{4}{9}$