On opposite sides of a wide vertical vessel filled with water (density ), two identical holes are drilled, each having cross-section area A . The height difference between holes is x . The resultant force of reaction of water flowing out of vessel is ( g = acceleration due to gravity)

Step-by-step solution

Let the depth of the upper hole from the free surface of water be h₁ and the depth of the lower hole be h₂ . The velocity of efflux from the upper hole is v₁ = 2gh₁ and from the lower hole is v₂ = 2gh₂ . The force of reaction due to water flowing out from a hole is given by the rate of change of momentum, F = v dm dt = A v^2 . The reaction force from the upper hole is F₁ = A (2gh₁) = 2 A g h₁ . The reaction force from the lower hole is F₂ = A (2gh₂) = 2 A g h₂ . Since the holes are on opposite sides, the water jets