Water is flowing at the rate of 15 kmh-1 through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?
Let the time taken by pipe to fill pond is t hours
As water flows 15 km in 1 hour, it will flow 15t meters in t hours.
Also,
Volume of cuboidal pond up to height 21 cm = Volume of water that passes through pipe in “t” hours
Now, For cuboidal pond
Length, l = 50 m
Breadth, b = 44 m
Height, h = 21 cm = 0.21 m
We know that,
Volume of tank = lbh
Where, l, b and h are the length, breadth and height of tank respectively
Volume of water = 50(44)(0.21) = 462 m3
For cylindrical pipe
Base diameter = 14 cm
Base radius, r = 7 cm = 0.07 m
[as radius = diameter/2]
Height, h = 15t km = 15000t m
[1 km = 1000 m]
As we know,
Volume of a cylinder = πr2h
Where r is base radius and h is the height of cylinder
Volume of water passed in pipe = π(0.07)2(15000t)
= 231t cm3
So, we have
231t = 462
t = 2 hours
Time required to fill tank up to a height of 25 cm is 2 hours.