# Water flows out through a circular pipe whose internal diameter is 2 cm,

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?

Solution:

Radius of the circular pipe $=0.01 \mathrm{~m}$

Length of the water column in $1 \mathrm{sec}=6 \mathrm{~m}$

Volume of the water flowing in $1 s=\pi r^{2} h=\pi(0.01)^{2}(6) \mathrm{m}^{3}$

Volume of the water flowing in $30 \mathrm{mins}=\pi(0.01)^{2}(6) \times 30 \times 60 \mathrm{~m}^{3}$

Let $h \mathrm{~m}$ be the rise in the level of water in the cylindrical tank.

Volume of the cylindrical tank in which water is being flown $=\pi(0.6)^{2} \times h$

Volume of water flowing in 30 mins $=$ Volume of the cylindrical tank in which water is being flown $\pi(0.01)^{2}(6) \times 30 \times 60=\pi(0.6)^{2} \times h$

$h=\frac{6(0.01)^{2} \times 30 \times 60}{0.6 \times 0.6}$

$h=3 \mathrm{~m}$