The cross – section of a pipe is 400 2
. It is used to fill a hemispherical tank of radius 3 m.
What must be the minimum flow rate of water in the pipe (in cm/sec) so that it can fill up the
tank in less than 20 minutes?
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3
Diameter of the cylindrical pipe = 7cm
∴ radius of pipe r=3.5cm
∴ area of cross section of cylindrical pipe = πr
2
=π(3.5)
2
Rate of water flow = 5 m/s
= 5×10 cm/s
= 500×60 cm/min
= 30000 cm/min
Volume of water discherged per min = π(3.5)
2
×30000cm
3
/min
= 1155000cm
3
/min
Volume of rectangular tank = (4×3×2.31)m
3
= 27.72m
3
= 27720000cm
3
∴ time taken to empty the rectangular tank by the pipe
=
1155000
27720000
min
= 24 min
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