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.
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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
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