Question

Water is flowing at the rate of 2.52km+hr through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40cm. If the increase in the level of water in the tank, in half an hour is 3.15m, find the internal diameter of the pipe.

Answer 1

I hope this will help you.

Answer 2

Given,

Level of tank in half  hour = 3.15 m

Level of  tank in  one hour  = 2× 3.15 = 6.3 m

Radius of tank = 40cm = 40/100 m = 4/10 m

Volume of  water  in tank in one  hour  V₁= π(4/10)²×6.3

Again,

Speed  of water  = 2.52 km/hr =2520km/hr. It means that  water   travels 2520 km in hour  in pipe.

Let the radius  of  pipe  be  r

Volume  of  water  through pipe one  hour ,V₂ = πr²×2520

Now,

V₁ = V₂

π(4/10)²×6.3 =  πr²×2520

16/100 × 6.3 = r² × 2520

r² = 1/2500

r = 1/50 m

r = 100/50 = 2 cm

Radius  of  pipe   = 2cm

Diameter  of pipe  = 4 cm