Question

water is flowing at the rate of 2.52 km/hr, through a pipe into a cylindrical tank of r=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

now volume of pipe is equal to volume of tank so radius is;

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