Question

Water is flowing at the rate of 2.5 km/h through a circular pipe of 20 cm internal diameter into a cistern of diameter 20 m and depth 2.5 m. In how much time will the cistern be filled?

Answer 1

Answer:

It will take 10 hour to fill the cristen.

Given:

• Water is flowing at the rate of 2.5 km/hr through a circular pipe of 20 cm internal diameter into a cistern of diameter 20 m and depth 2.5 m

To find:

• How long will take to cistern be fully filled.

Solution:

For cistern,

Diameter (d) = 20 m

Hence, radius (r) = 10 m

Height (h) = 2.5 m

Volume of cistern = πr²h

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3.14 × 10² × 2.5

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 7.85 × 100

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 785 m²

To fill the cistern to with water the circular pipe must also have same volume of water.

For circular pipe,

Diameter = 20 cm = 0.2 m

Hence, Radius (R) = 0.1 m,

Height (H) = ?

Volume of circular pipe = πR²H

785 = 3.14 × (0.1)² × H

H = (785×100)/3.14

H = 25000 m = 25 km

Now, here hight = length = distance

Speed = 2.5 km/hr

We know, Time = Distance/Speed

Therefore, Time = 25/2.5 = 10 hr

Hence, it will take 10 hour to fill the cristen.