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Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. The rise in the level of water in 30 minutes is
- a)3 m
- b)– 3 m
- c)6 m
- d)– 6 m
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Water flows out through a circular pipe whose internal diameter is 2 c...
Internal diameter of the pipe = 2 cm
So its radius = 1cm = 1/100 m
Water that flows out through the pipe in 6 ms–1
So volume of water that flows out through the pipe in
∴ In 30 minutes, volume of water flow
This must be equal to the volume of water that rises in the cylindrical tank after 30 min and height up to which it rises say h.
Radius of tank = 60 cm = 60/100 m
So required height will be 3 m.
So its radius = 1cm = 1/100 m
Water that flows out through the pipe in 6 ms–1
So volume of water that flows out through the pipe in
∴ In 30 minutes, volume of water flow
This must be equal to the volume of water that rises in the cylindrical tank after 30 min and height up to which it rises say h.
Radius of tank = 60 cm = 60/100 m
So required height will be 3 m.
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Community Answer
Water flows out through a circular pipe whose internal diameter is 2 c...
Given Data:
- Internal diameter of the circular pipe = 2 cm
- Rate of water flow = 6 m/s
- Radius of the base of cylindrical tank = 60 cm
- Time taken = 30 minutes
Calculations:
1. Convert the time from minutes to seconds:
30 minutes = 30 x 60 seconds = 1800 seconds
2. Calculate the volume of water flowing in 30 minutes:
Volume = Area of pipe x Speed x Time
Area of pipe = πr^2 (r = radius = diameter/2)
Area = π(1 cm)^2 = π cm^2
Volume = π x 1800 x 6 cm^3 = 10800π cm^3
3. Convert the volume to cubic meters:
1 m^3 = 1000000 cm^3
Volume = 10800π / 1000000 m^3 = 0.0108π m^3
4. Calculate the rise in water level in the cylindrical tank:
Volume = πr^2h (h = rise in water level)
0.0108π = π(60 cm)^2h
0.0108 = 3600h
h = 0.0108 / 3600 = 0.000003 m = 0.003 m
Conclusion:
The rise in the level of water in the tank after 30 minutes is 0.003 meters or 3 millimeters. Therefore, the correct answer is option A.
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Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. The rise in the level of water in 30 minutes isa)3 mb)– 3 mc)6 md)– 6 mCorrect answer is option 'A'. Can you explain this answer?
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