Water is flowing at the rate of 2.52 km per hour through a cylindrical pipe into cylindrical tank the radius of whose base is 40 cm in the increase in the level of the water in the tank in half an hour is 3.5 m find the interval diameter of the pipe
Answers
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Answer:
Increase in the water level in half an hour = 3.25 m = 325 cm
Radius of the water tank = 40 cm
Volume of the water that falls in the tank in half an hour = πr
2
h=
7
22
×40×40×325=1634286 cu cm
Rate of the water flow = 2.52 km/hr
Length of water column in half an hour =
60
(2.52×30)
=1.26 km=126000 cm
Let the internal diameter of the cylindrical pipe be d.
Volume of water that flows through the pipe in half an hour = π×(
2
d
)
2
×126000
As we know that,
Volume of the water that flows through pipe in half an hour = Volume of water that falls in the cylindrical tank in half an hour
⟹
7
22
×(
2
d
)
2
×126000=1634286
⟹
7
22
×
4
d
2
×126000=1634286
⟹d
2
≈16 ⟹d=4cm
So, the internal diameter of the pipe is 4 cm