Question

Water is flowing at the rate of 14 km/hr through a circular pipe of internal diameter is 5cm
as shown in the picture. Use pi = 22/7
The water fills a cuboidal tank of dimensions 5 m x 5 m x 2 m. Find
1) The height of the water level when it fills the tank in 10 mins.

2) In what time will the water tank be filled 1m if the speed of water flowing is 7 km/hr.

3) How many days the water in the tank can be used if 10000 litres of water are used per
day?

Answer 1

Answer:

Suppose the level of the water in the tank will rise by 7cm in x hours.

Since the water is flowing at the rate of 5km/hr.

Length of the water column in x hours =5x km=5000x metresClearly, the water column forms a cylinder whose radius r=

2

14

cm=

100

7

m

Length =h=5000x metres

Volume of the water flowing through the cylindrical pipe in x hours

=πr

2

h

=

7

22

×(

100

7

)

2

×5000xm

3

=77xm

3

Also,

Volume of the water that falls into the tank in x hours =50×44×

100

7

m

3

=154m

3

But, the volume of the water flowing through the cylindrical pipe in x hours = Volume of the water that falls in the tank in x hours.

⇒77x=154⇒x=2

⇒x=

77

154

=2 hours