A closed pipe containing liquid showed a pressure P₁ by gauge. When the valve was opened, pressure was reduced to P₂ . The speed of water flowing out of the pipe is ( =density of water)

Step-by-step solution

Using Bernoulli's equation for horizontal flow: P₁ + 1 2 v₁^2 = P₂ + 1 2 v₂^2 Initially, the valve is closed, so the velocity of water v₁ = 0 . When the valve is opened, the pressure becomes P₂ and the velocity becomes v₂ = v . Substituting these values into the equation: P₁ + 0 = P₂ + 1 2 v^2 P₁ - P₂ = 1 2 v^2 v^2 = 2(P₁ - P₂) v = [ 2(P₁ - P₂) ]^ 1 2 Answer: [ 2(P₁ - P₂) ]^ 1 2