Question

Water flows at a speed of 1.0 m/s through a hose whose internal diameter is 10 mm. What should the diameterof the nozzle be if the water is to emerge at 5.0 m/s?

Answer 1

The continuity of flow equation says

$$v_1A_1=v_2A_2$$

or

$$v_1d_1^2=v_2d_2^2$$

Hence,

$$d_2=d_1\sqrt{\frac{v_1}{v_2}}=10\:\rm mm*\sqrt{\frac{1.0\:\rm m/s}{5.0\:\rm m/s}}=4.5\:\rm mm$$