Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10 m and dep…

Let the time taken to fill the cistern be‘t’ hr.

Given, Diameter of cistern is 10m and depth is 2m.

We know that, Volume of cylinder = πR2 × h

⇒ Radius of cylinder = Diameter/2

= 5 m

∴ Volume of cylinder = π × 52 × 2 m3

= 50π m3

Given, Velocity of water = 3 km/hr

= 3000 m/hr (? 1 km = 1000 m)

Inner diameter of pipe = 20 cm

∴ Inner radius = 20/2 = 10 cm

= 0.1 m (? 1m = 100 cm)

∴ Volume flow rate of water = π × (inner radius)2 × velocity of water

= π × 0.12 × 3000 m3/hr

= 30π m3/hr

Now,

⇒Time taken to fill the cistern $(,t = \frac{{Volume\ of\ cistern}}{{Volume\ flow rate}})$

$(\Rightarrow t = \frac{{50{\rm{\pi }}}}{{30{\rm{\pi }}}}\ {\rm{hr}})$

⇒ t = 1.67 hours

Or, t = 1 hr 40 minutes