A fountain produces a vertical jet of water, which rises to a height of 30 m before falling back into a pond. If the jet of water is produced by a nozzle whose velocity coefficient is 0.95, find the pressure with which the water is fed into the nozzle. You may assume that the jet of water is not affected by friction once it has left the nozzle and that there is a negligible change in the potential energy of water as it passes through the nozzle.
Tackle the problem by splitting it into two parts: (i) from the entry to the nozzle to a point just after the water has left the nozzle; (ii) from just after the water has left the nozzle to the top of the water jet. Analyse part (ii) first noting that the flow is frictionless and that the pressure is atmospheric everywhere. Prove that the velocity just after the nozzle is 24.26 m/sec and then analyse the flow through the nozzle itself.