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Q.

Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in the level of water in the tank in half hours.

Grade: Grade

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a

45 cm

b

35 cm

c

25cm

d

55 cm

answer is A.

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Detailed Solution

The figure of the system can be drawn as:

The inner diameter of the cylindrical tube is equal to 2 cm
Radius(r) = 1 cm
Now it is given that the radius of the base of the cylindrical tank is 40 cm and the velocity of water flow through the cylindrical pipe is 0.4 m/s.
Water flows through a cylindrical pipe at a speed of 0.4 m per 1 second
So the volume of water flowing in the pipe =

π r 2 H

⇒ π (1) 2 × 0.4 × 100 c m 3

So the volume of water which is flowing through the pipe in 30 minutes that is 30x60 sec is

⇒ π (1) 2 × 0.4 × 100 × 30 × 60........... (1)

Let H be the height of cylindrical tank so its volume is given as

π R 2 H

where R=40 cm
So the volume of water in the cylindrical tank after 30 minutes =

…………. (2)
Since the water from the pipe flows into the tank, equation 1 should equal equation 2.

⇒ π (1) 2 × 0.4 × 100 × 30 × 60

On solving we get, H = 45cm.

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Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in the level of water in the tank in half hours.Grade: Grade