Question

Water is flowing at 0.7m/s through a circular pipe of internal diameter of 2cm into cylindrical tank,the radius of whose base is 40cm. Find the increase in water level in 30 minutes

Answer 1

Let Water level rise in 0.5 hr  =  x cm
And
We know Volume of cylinder  = , So
Here Radius  r  =  1  cm   and h =  0.7 m  = 70 cm  (  As we know 1 m  =  100 cm   )

As given Water is flowing at the rate of  0.7 m per sec
So,
Volume of water flowing through the pipe in one sec = 
In 0.5 hours, water flowing through the pipe =   (  We know 1 hour = 60 minutes and 1 minute = 60 sec , So 0.5 hr = 30 minutes =  1800 sec )

Volume of water in the tank after 0.5 hours = Volume of the cylindrical tank the radius of whose base is 40 cm and height is x cm ( as we assumed )

So,
Volume of the cylindrical tank  =  
So,


So,
Water level rise in 0.5 hr  = 78.75 cm                                  ( Ans )

Answer 2

The volume of water raised after 30 mins in the tank is given as 395.64 litres

Given :

Diameter of cylindrical pipe = 2cm

The rate of water flow = 0.7m/sec

To Find :

Much water rise in the tank in half and hour

Formula Applied :

$volume \:\:of \: water \: flowing \: through\ \:pipe= Cross \:sectional\: area\: of \:pipe \times Rate\: of\:flow \:\:of\:water$

Solution :

As by given ,

Cross section area of pipe =Area of circle=$\pi r^{2}$

Diameter of pipe = 2cm

Radius = $\frac{diameter}{2} = \frac{2}{2} =1cm$

Area of circle =$\pi r^{2} = \frac{22}{7} \times 1\times1= 3.14 cm^{2}$

Hence the volume of water flowing per second ,

$\implies volume = Cross\:section\:area\times rate\:of\:flow$

$\implies Volume=3.14cm^{2} \times 0.7m/s$

$\implies 3.14 cm^{2} \times 70cm/s\:\:\:\:\: (\because 1m=100cm)$

$\implies volume= 219.8cm^{3} m/s$

Hence $219.8cm^{3}$of water is flowing per second.

The amount of water flowing for 30 mins is given as,

$\begin{gathered}\implies 30\times60\times219.8 \:\:\:\:\: ( \because 1 min = 60 seconds)\\\end{gathered}$

$\implies 395640 \: cm^{3}$

$\implies1cm^{3} = 0.001 \: litres$

Hence the volume of water raised after 30 mins in litres is given as 395.64 litres