The density of a liquid contained in a tank of area 0.5 m 2 is 1200 k g m - 3 . The container is closed by a massless, frictionless and movable piston and there is a hole of area 1 c m 2 near the bottom of the container. A load of 30 k g is placed on the piston and the height of liquid level is 75 c m above the bottom. What is the initial flow velocity (in m s - 1 ) of the liquid? [Take, g = 10 m s - 2 ]

Step-by-step solution

Let the velocity of efflux at point 2 is v . Given, a = 1 c m 2 , A = 0.5 m 2 = 0.5 × 10 4 c m 2 Applying continuity equation, A V = a v V = a A v Since, a ≪ A , V ≪ v , V 2 is negligible. Pressure at (1), p 1 = p 0 + m g A = p 0 + 30 × 10 0.5 = p 0 + 600 Pressure at (2) , p 2 = p 0 where, p 0 is atmospheric pressure. Applying Bernoulli's equation between (1) and (2), p 1 + ρ g h + 1 2 ρ V 2 = ρ 2 + 1 2 ρ v 2 V 2 is negligible, then p 0 + 600 + 1200 × 10 × 0.75 = p 0 + 1 2 × 1200 v 2 600 v 2 = 9600 ⇒ v 2 = 16 ⇒ v =