Question

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

Answer 1

$$\begin{gathered} \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{circular}\mathrm{pipe}=0.01\mathrm{m} \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{column}\mathrm{in}1sec=6\mathrm{m} \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{flowing}\mathrm{in}1s=\mathrm{\pi }{r}^{2}h=\mathrm{\pi }(0.01{)}^2(6){\mathrm{m}}^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{flowing}\mathrm{in}30\mathrm{mins}=\mathrm{\pi }(0.01{)}^2\left(6\right)\times 30\times 60{\mathrm{m}}^3 \\ \mathrm{Let}\mathit{}h\mathrm{m}\mathrm{be}\mathrm{the}\mathrm{rise}\mathrm{in}\mathrm{the}\mathrm{level}\mathrm{of}\mathrm{water}\mathrm{in}\mathrm{the}\mathrm{cylindrical}\mathrm{tank}. \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{tank}\mathrm{in}\mathrm{which}\mathrm{water}\mathrm{is}\mathrm{being}\mathrm{flown}=\mathrm{\pi }(0.6{)}^2\times h \\ \mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{flowing}\mathrm{in}30\mathrm{mins}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{tank}\mathrm{in}\mathrm{which}\mathrm{water}\mathrm{is}\mathrm{being}\mathrm{flown} \\ \mathrm{\pi }(0.01{)}^2\left(6\right)\times 30\times 60=\mathrm{\pi }(0.6{)}^2\times h \\ h\mathit{=}\frac{6(0.01{)}^2\times 30\times 60}{0.6\times 0.6} \\ h\mathit{=}3\mathrm{m} \end{gathered}$$