How to calculate time of water filling a cistern?

Question

Water  is flowing at the rate of 3km/hr through a circular pipe of 20 cm internal diameter into circular cistern of diameter 10 m and depth 2m.In how much time will the cistern be filled?

Answer 1

1 hour and 45 min

Answer 2

 

Here is the answer to your question.

Let the time required to fill the cistern be 't ' hours.

Diameter of the cistern = 20 m

∴ Radius of the cistern =  = 10 m

Volume of the cistern = πr ² h

Diameter of the pipe = 20 cm = 0.2 m

∴ Radius of the pipe (r) = = 0.1 m

Cross section area of pipe = πr ²

Rate of flow of water through pipe = 2.5 km/h = 2500 meter/hour

Volume of the cistern = Cross-section area of pipe * Rate of flowing of water through pipe * t

⇒ t = 10 hours

Hence, the cistern will be filled in 10 hours.

 

Answer 3

In order to understand the solution of this problem, you must understand a few concepts related to the same.

Firstly, Time=Distance x Speed

The area of a cyclinder(Pipe & Cistern)=Pi r^2 h, where r is the radius and h is the height of the cylinder

Here we do not know the height of the cylinder but we do know the speed with which the water is flowing

Therefore, the Height of the cylinder will be substituted with the Speed x Time as aforementioned.

The volume flowing through the pipe will be equal to that of the cylinder; therefore, we can equate the two in the following manner:

pi r^(2)h=pir2^(2)h2

where r and h is the radius and height of the pipe respecitvely and r2 and h2 is the radius and height of the cistern respectively.

r=(20cm Diameter=10cm radius since d=2r)10/100 m=1/10m

Speed=3km/h=3000m/h

Time=h number of hours

r2=(10m Diameter=5cm Radius since d=2r)5m

h2=2m

Subsituting and Equating:

1/10 x 1/10 x 3000m/1 x h=5 x 5 x 2

30m x h=50m

h=50m/30m

h=5/3

Therefore, it will take 5/3 hours to fill the cistern. Otherwise, multiplying by 60 to convert into minutes:

5/3 x 60= 5 x 20= 100 minutes=1 hour and 40 minutes.

Therefore, the pipe will take 1 hour and 40 minutes to fill the cistern.

Cheers.