Question

Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minute. Find the rate of flow of water in the pipe in km/hr.

Answer 1

Given:

Inner diameter = 7 cm ⇒ radius r = 3.5 cm.

Volume collected = 192.5 litres/min.

Step-wise calculation:

1. Convert volumetric flow to cm³ per hour:

192.5 L/min = 192.5 × 60

= 11,550 L/hr

1 L = 1000 cm³

⇒ Volume per hour = 11,550 × 1000

= 11,550,000 cm³/hr

2. Volume of water in one hour = Volume of a cylindrical column of length h (cm) and radius 3.5 cm:

Area = `πr^2 = (22/7) × (3.5)^2`

= `(22/7) xx 12.25`

= 38.5 cm²

Volume = Area × h

= 38.5 × h cm³

3. Equate volumes and solve for h:

38.5 × h = 11,550,000

`h = (11,550,000)/(38.5)`

= 3,00,000 cm

4. Convert h to km/hr (linear distance travelled by water in one hour = speed):

3,00,000 cm = 3,000 m = 3 km.

Therefore speed = 3 km/hr.

The rate of flow of water in the pipe is 3 km/hr.