Question

Water is flowing in a pipe of diameter $4 \,cm$ with a velocity $3 \,m/s$. The water then enters into a pipe of diameter $2 \,cm$. The velocity of water in the other pipe is:

• A. 3 m/s
• B. 6 m/s
• C. 12 m/s
• D. 8 m/s

Answer 1

Answer: (C)

According to principle of continuity, when an incompressible and non-viscous liquid flows in a streamlined motion through a tube of non-uniform cross-section, then the product of the area of cross-section and the velocity of flow is same at every point in the tube.
Thus, $ Av\text{ }= $ constant or
$ {{A}_{1}}{{v}_{1}}={{A}_{2}}{{v}_{2}} $
or $ \pi {{r}_{1}}{{\,}^{2}}{{v}_{1}}=\pi {{r}_{2}}{{\,}^{2}}{{v}_{2}} $
Given, $ {{r}_{1}}=\frac{4}{2}cm=0.02\,m, $
$ {{r}_{2}}=\frac{2}{3}cm=0.01\,m, $
$ {{v}_{1}}=3\,m/s $
$ \therefore $ $ \pi {{(0.02)}^{2}}\times 3=\pi {{(0.01)}^{2}}{{v}_{2}} $
or $ {{v}_{2}}={{\left( \frac{0.02}{0.01} \right)}^{2}}\times 3 $
$ =12\,\,m/s $