Question

Water flowing at the rate of 0.7m/s through a circular pipe whose internal diameter is 2 cm into a cylindrical tank , the radius of whose base is 40 cm . Determine the increase in level of water in an hour

Answer 1

Let Water level rise in 0.5 hr  =  x cm
And
We know Volume of cylinder  = π r2h , So
Here Radius  r  =  1  cm   and h =  0.7 m  = 70 cm  (  As we know 1 m  =  100 cm   )

As given Water is flowing at the rate of  0.7 m per sec
So,
Volume of water flowing through the pipe in one sec = 227 × 1 × 1× 70 =  22 × 10 = 220 cm3
In 0.5 hours, water flowing through the pipe = 1800 × 220 = 396000 cm3  (  We know 1 hour = 60 minutes and 1 minute = 60 sec , So 0.5 hr = 30 minutes =  1800 sec )

Volume of water in the tank after 0.5 hours = Volume of the cylindrical tank the radius of whose base is 40 cm and height is x cm ( as we assumed )

So,
Volume of the cylindrical tank  =  227 × 40 × 40× x= 35200 x7cm3
So,

35200 x7 = 396000⇒x = 396000 × 735200⇒x = 11.25 × 7⇒x =78.75
So,
Water level rise in 1 hr  = 157.5 cm                                  ( Ans )