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.

Answer 1

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.