Question

Water is flowing through a cylindrical pipe of internal diameter 2cm into a cylindrical tank of base radius 40cm at the rate of 0.7m/sec .By how much will the water rise in the tank in half an hour?​

Answer 1

Step-by-step explanation:

Given diameter of the circular pipe = 2 cm

So, the radius of the circular pipe = 2/2 = 1 cm

Height of the circular pipe = 0.7 m = 0.7 * 100 = 70 cm

Now, volume of the water flows in 1 second = πr2 h

                                                                = 3.142 * 12 * 70

                                                                = 3.142 * 70

Volume of the water flows in 1/2 hours =  3.142 * 70 * 30 * 60

Now, volume of the water flows = Volume of the cylinder

=> 3.142 * 70 * 30 * 60 = πr2 h

=> 3.142 * 70 * 30 * 60 = 3.142 * (40)2 h

=> 70 * 30 * 60 = 40 * 40 * h

=> h = (70 * 30 * 60)/(40 * 40)

=> h = (70 * 3 * 6)/(4 * 4)

=> h = 1260/16

=> h = 78.85 cm

So, the level of water rise in the tank in half an hour is 78.75 cm

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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 ,

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

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

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

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

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

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

 $\implies 30\times60\times219.8 \:\:\:\:\: ( \because 1 min = 60 seconds)$

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

$1cm^{3} = 0.001 \: litres$

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