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Question

Water is flowing at the rate of 7 meters per second through a circular pipe whose internal diameter is 2cm into a cylindrical tank the radius of whose base is 40cm. Determine the increase in the water level in 12 hour.

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Solution

We have

Rate of flow of water =7m/sec=700cm/sec

Length of the water column in 12hours=(700×30×60)cm

Clearly water column forms a cylinder of radius 1cm and length (700×30×60)cm

volume of the water that flows in the tank in 12hour

=(227×1×1×700×30×60)cm3 ........(i)

Let h cm be the rise in the level of water in the tank.
Then, volume of the water in the tank =227×40×40×hcm3 .......(ii)

From (i) and (ii) we have

227×40×40×h=227×1×1×700×30×60

h=787.5788cm

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