Question

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

Answer 1

Answer:

20 minutes or 1200 sec

Step-by-step explanation:

speed of flowing water = 3 km / hr

so we will convert speed in metre/sec

1 km = 1000m , 1 hr = 60*60 sec

3 * 1000m/60*60sec

3*5/18 m /s ⇒ 5/6   m / sec

diameter of circular pipe =  20cm so radius = 10 cm (r=d/2)

radius in metres = 10/100 = 0.1 m

here speed of water would act as height of pipe

volume of water flowing through pipe in 1 sec

π r²h     ⇒ 22*1*1*5/7*10*10*6 ⇒ 110/ 4200 ⇒ 11/420 m³

so, 11/420 m³ takes 1 sec ,    so 1m³ will take 1/11/420 sec ⇒ 1m³ = 420/11 sec

r of cistern = 5 m

height = 2m

now, volume of water collected in 1 sec in cistern

πr²h ⇒  22*5*2 / 7 ⇒220/7 m³

as stated 1m³ =420/11 sec

so   220/7 m³ will take

220*420/7*11  

1200 sec

1 sec = 1/60 min

so 1200 sec would take 1200/60

20

time taken = 20 minutes