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Water flows out through a circular pipe whose internal diameter is 2 cm at the rate of 6 metre 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.

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3 m

-3 m

6 m

-6 m

answer is A.

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Detailed Solution

Internal pipe diameter=2 cm
Pipe’s internal radius

r_{i} = \frac{d}{2} = \frac{2}{2} = 1 cm

The water's flow rate
q=6 m/sec
q=600 m/sec (1 m = 100 cm)
Base of cylindrical tank's radius

r = 60 cm

Total time t= 30 minute=30

\times

60 sec
Rise in height in cylindrical tank

= \frac{rate of flow of water \times total time \times volume of pipe}{volume of cylindrical tank}

= \frac{q \times t \times π \times r_{i}^{2}}{π \times r^{2}}

= \frac{600 \times 30 \times 60 \times π \times 1 \times 1}{π \times 60 \times 60}

= 1080000 / 3600

= 300 cm

= 3 m

(100 cm = 1 m)
So, rise in water level = 3 m.
Option 1 is correct.

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