Question

water flows through a circular pipe whose internal diameter is 2 centimetre at the rate of 6 m per second into cylindrical tank the radius of whose base is 60 cm find the rise in level of water in 30 minutes

Answer 1

Internal Diameter = 2cm
Internal Radius = 2/2 cm = 1 cm
Velocity of water = 6 m/s = 600 cm/s

Volume = Base area of pipe x Rate of water flows

$= > v \: \: = \pi \: {r}^{2} \times rate$

$= > v \: \: = \frac{22}{7} \times 1 \times 1 \times 600$

$= > \: v \: \: = \frac{22 \times 600}{7} \: {cm}^{3}$

Now, Volume of Water flow in 30 mins
As we know that 30 min = (30 x 60)s = 1800s

$= > v \: \: = \frac{22 \times 600}{7} \times 1800 \: {cm}^{3}$
Again,

=> Volume of water in Tank = Volume of water flow in 30 min or 1800 s.


$= > \pi \: {r}^{2} h = \frac{22 \times 600}{7} \times 1800$

$= > \frac{22}{7} \times 60 \times 60 \times h = \frac{22 \times 600}{7} \times 1800$

$= > 60 \times 60 \times h = 600 \times 1800$

$= > h \: \: = \frac{600 \times 1800}{60 \times 60}$

$= > h \: \: \: = 300 \: cm \:$

$= > \: h \: \: = \frac{300}{100} \: m$

$= > h \: \: = \: 3 \: m \:$


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