• # question_answer ) Water is flowing through a cylindrical pipe of cross-section area $0.0971\text{ }{{m}^{2}}$ at a speed of$1.0\text{ }m/s$. If the diameter of the pipe is halved, then find the speed of flow of water through it- A) $4.0\text{ }m/s$                       B) $6.0\text{ }m/{{s}^{2}}$C) $4.0\text{ }m/{{s}^{2}}$                   D) $6.0\text{ }m/s$

${{A}_{1}}=0.09\text{ }\pi {{m}^{2}},~~~~{{\nu }_{1}}=1\text{ }m/s$ $=\pi {{r}^{2}}$ ${{A}_{2}}=\pi {{\left( r/2 \right)}^{2}}\,\,{{\nu }^{2}}=?$ ${{A}_{1}}{{\nu }_{1}}={{A}_{2}}{{\nu }_{2}}$ $(\pi {{r}^{2}})=\frac{\pi {{r}^{2}}}{4}{{\nu }^{2}}$ ${{V}_{2}}=4\text{ }m/s$