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?

Answer 1

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.