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Water is flowing at the rate of $5 kmph$ through a pipe of diameter 14cm into a rectangular tank, which is $50 m$ long and $44 m$ wide. Determine the time in which the level of water in the tank will rise by $7 cm$ .

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6hours

4hours

3hours

2hours

answer is D.

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Detailed Solution

Given flow rate through a pipe of diameter 14cm is 5kmph.
Volume of the cylinder

= π r 2 h

Assume that the level of water in the tank will rise by 7 cm in

x

hours.
Thus, its length in x hours is,

⇒ 5 x ⇒ 5000 x meters

Water column forms a cylinder whose radius is,

r = 142 c m ⇒ r = 7100 m

Volume of water flowing through the cylindrical pipe in

x

hrs,

⇒ π r 2 h ⇒ 227 × 71002 × 5000 x ⇒ 77 x m 3

Volume of water that falls into tank,

⇒ 50 × 40 × 7100 m 3 ⇒ 154 m 3

Now,
Volume of water flowing through the cylindrical pipe in x hrs = Volume of water that falls in a tank in x hrs.

⇒ 77 x = 154 ⇒ x = 15477 ⇒ x = 2 h r s

Thus, the time in which the level of water in the tank will rise by 7 cm is 2 hours.
Therefore, option (4) is correct.

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