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Question
Water is flowing at the rate of 6 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 60 m long and 22 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.
Solution
We have,
speed of the water flowing though the pipe ,H=6 Km/h `= (600000 "cm")/"3600 s" = 500/3 "cm"// "s"`
Radius of the pipe, R = `14/2` = 7 cm
Length of the rectangulat tank, l = 60 m = 6000 cm
Breadth of the rectangular tank, b = 22 m = 2200 cm and
Rise in the level of water in the tank, h = 7 cm
Now,
Volume of the water in the rectangular tank = lbh
= 6000 × 2200 ×7
=92400000 cm3
Also,
Volume of the water in the flowing through the pipe im 1s = πR2H
`= 22/7xx7xx7xx500/3`
`=77000/3 "cm"^3`
so,
`"The time taken" ="Volume of the water in the rectangular tank"/"Volume of the water flowing through the pipe in 1 s"`
`=92400000/((77000/3)`
`= (92400xx3)/77`
=3600 s
= 1 hr
So, the time in which the level of water in the tank will rise by 7 cm is 1 hour.
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