Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of 5 × 10 5 N is applied an the top surface of water using a piston. The speed of efflux from the hole will be : (given atmospheric pressure P A = 1 . 01 × 10 5 P a , density of water ρ w

Step-by-step solution

Assuming there is no atmospheric pressure on piston, P 1 = F π R 2 and P 2 = P 0 . Applying Bernoulli's equation at point 1 and 2 , p 1 + ρ g h 1 + 1 2 ρ v 1 2 = p 2 + ρ g h 2 + 1 2 ρ v 2 2 ⇒ F π R 2 + ρ g h 1 - h 2 = P 0 + 1 2 ρ v 2 2 ⇒ v 2 = 2 F π R 2 ρ - 2 P 0 ρ + 2 g h 1 - h 2 v 2 = 2 × 5 × 10 5 3 . 14 × 1 2 × 1000 - 2 × 1 . 01 × 10 5 1000 + 2 × 10 × 10 ≈ 17 . 8   m   s - 1