Question:
Water is flowing at the rate of 7 metres per second through a circular pipe whose internal diameter is 2 cm into a cylindrical tank the radius of whose base is 40 cm. Determine the increase in the water level in 1/2 hour.
Answer:
Given rate of flow of water = 7 m = 700 cm
Length of pipe in which the water has traveled in half hour h = 700*30*60 = 1260000 cm
Internal radius of the pipe r = 2/2 = 1 cm
Radius of the cylinder R = 40 cm
Let the height of the water in the cylindrical tank is H
Now,
Volume of the water coming out of the pipe = Volume of the water collected in the cylindrical tank
=> πr2 h = πR2 H
=> r2 h = R2 H
=> 1*1260000 = (40)2 H
=> 1260000 = (40)2 H
=> 1260000 = 1600H
=> H = 1260000/1600
=> H = 12600/16
=> H = 787.5 cm
=> H = 787.5/100 cm
=> H = 7.875 m
So, the increase in the water level in 1/2 hour is 7.875 m
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