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Question
Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?
Solution
Given, radius of tank, r1 = 40 cm
Let height of water level in tank in half an hour = 1 cm.
Also, given internal radius of cylindrical pipe, r2 = 1 cm
And speed of water = 80 cm/s
i.e., in 1 water flow = 80 cm
In 30 (min) water flow = 80 × 60 × 30
= 144000 cm
According to the question,
Volume of water in cylindrical tank = Volume of water flow from the circular pipe in half an hour
⇒ `pir_1^2h_1 = pir_2^2h_2`
⇒ `40 xx 40 xx h_1 = 1 xx 1 xx 44000`
∴ `h_1 = 144000/(40 xx 40)`
= 90 cm
Hence, the level of water in cylindrical tank rises 90 cm in half an hour.
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