Q. 244.0( 32 Votes )

Water is flowing through a cylindrical pipe of internal diameters 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in level of water in tank in half an hour.

Answer :

Given,


Diameter of the cylindrical pipe = 2 cm
Radius of the cylindrical pipe = 1 m
Height of the cylindrical pipe = 0.4m/s = 40 cm/s

Water flown in 1 sec = 40 cm
Water flown in 30 minutes (30 × 60 seconds) 
= 40 × 60 × 30 m = 72000 cm

Radius of cylindrical tank = 40 cm
Let Height be h,
As we can see the volume of water which passes through the cylindrical pipe is equal to the volume of water present in the cylindrical tank after half an hour.
So,

Volume of water which passes through the cylindrical = volume of water present in the cylindrical tank after half an hour
πr2h = πr2h
(1)2 × 72000 = (40)2 × h
72000 = 1600 × h
h = 45 cm


Hence,

The rise in level of water in tank in half an hour will be 45 cm.

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