Problem 1: Water flows through a 1 cm diameter pipe with a speed of 1 ms^-1. What should be the diameter of the nozzle if the water is to emerge at 2.1 ms^-1.

Solution

Given data                    Diameter of the pipe                      = D₁ = 1 cm = 0.01 m

                                             Speed of water in pipe                   = v₁ = 1 ms^-1

                                             Speed at the nozzle of the pipe    = v₂ = 2.1 ms^-1

Required                        Diameter of the nozzle                   = D₂ =?

Formula

Equation of continuity. Now if A₁ is the cross-sectional area of the pipe and A₂ is the cross-sectional area of the nozzle, then

Put these values in the formula.