Water is flowing at the rate of 10km/hr through a pipe of diameter 16cm into a cuboidal tank of dimension 22m x 20m x 16m . how long it will take to fill empty tank ?
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35 hours time is taken to fill the empty tank.
Water is flowing at the rate of 10km/hr through a pipe of diameter 16cm into a cuboidal tank of dimension 22m x 20m x 16m.
We have to find the time taken to fill the empty tank.
Water flowing at the speed , v = 10 km/h
Let after t hours, the empty tank is completely filled.
So, length covered by water , l = speed of flowing of water × time
= 10t km = 10,000t m [ ∵ 1 km = 1000 m]
diameter of pipe, d = 16 cm
∴ radius of pipe, r = d/2 = 8 cm = 0.08 m
∴ volume of water flowing through pipe in t hours, V = πr²l
= 3.14 × 0.08 × 0.08 × 10000t
= 200.96 t m³
And volume of cuboidal tank, V = l × b × h
= 22 m × 20 m × 16 m = 7040 m³
Here, volume of water flowing through pipe in t hours = volume of cuboidal tank
⇒200.96 t = 7040
⇒t = 7040/200.96 = 35.03 ≈ 35 hrs