Water flows through a horizontal pipe at a speed 'V'. Internal diameter of the pipe is 'd'. If the water is emerging at a speed ' V₁ ' then the diameter of the nozzle is

Step-by-step solution

According to the equation of continuity, the volume flow rate of an incompressible fluid remains constant throughout the pipe. A₁ V₁ = A₂ V₂ Let the diameter of the nozzle be d₁ . The cross-sectional area of the pipe is A₁ = d^2 4 and the cross-sectional area of the nozzle is A₂ = d₁^2 4 . Substituting the values into the equation of continuity: d^2 4 V = d₁^2 4 V₁ d^2 V = d₁^2 V₁ d₁^2 = d^2 V V₁ d₁ = d V V₁ Answer: d V V ₁