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Question
Water flows through a cylindrical pipe of internal diameter 7 cm at 36 km/hr. Calculate the time in minutes it would take to fill the cylindrical tank, the radius of whose base is 35 cm, and height is 1 m.
Solution
Radius of pipe = `7/2` cm
Rate of water flow = 36 km/h
= `36 xx 5/18` m/s
= 10 m/s
= 10 x 100 cm/s
= 1000 cm/s
∴ Volume of water flowing in 1 second = πr2h
= `π xx 7/2 xx 7/2 xx 1000` cm3
= π x 7 x 7 x 250 cm3 ....(1)
Radius of tank (R) = 35 cm
Height of tank (H) = 1 m = 100 cm
∴ Volume of tank = πr2H
= π x 35 x 35 x 100 cm3 ...(2)
∴ Time taken to fill the tank = `"Volume of tank"/"Volume of water flowing in 1 second"`
= `(π xx 35 xx 35 xx 100)/(π xx 7 xx 7 xx 250)` seconds
= 10 seconds
= `10/60` minute
= `1/6` minute.
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