A large closed cylindrical tank contains water. At a certain instant, the air trapped above the water surface is at a pressure of 2p₀ (where p₀ is the atmospheric pressure) and has a height h₀ . Water flows out from a hole in the tank wall located at a depth h₁ below the top. A long vertical tube, open to the atmosphere, is connected to the lower part of the tank. Assuming the density of water is , calculate the init

Step-by-step solution

Let us apply Bernoulli's principle between the free surface of the water inside the tank and the point just outside the hole. At the free surface of the water inside the tank: Pressure, P₁ = 2p₀ Velocity, v₁ 0 (since the tank is large) Height of the water surface from the hole, h = h₁ - h₀ At the hole (just outside): Pressure, P₂ = p₀ (atmospheric pressure) Velocity of efflux, v₂ = v According to Bernoulli's equation: P₁ + 1 2 v₁^2 + g h = P₂ + 1 2 v₂^2 + 0 Substituting the values, we get: 2p₀ + 0 + g (h₁ - h₀) = p