An impressive outdoor fountain emits a continuous, vertical jet of water into the air. The jet emerges from a cylindrical nozzle 3 cm in diameter and carries 2.3 gal/s of liquid. A pump is used to move fluid to the nozzle through a 6 cm diameter hose that is connected to a reservoir (pool) of water. Assume that water is incompressible and that the pressure and temperature of the jet immediately outside of the nozzle is very close to that of the reservoir. Neglect any heat transfer.
a) What is the velocity of the water jet leaving the nozzle, in m/s? What is the velocity of the water entering the hose from the reservoir, in m/s?
b) How much power is required to operate the pump, in W?
c) How high will the jet reach, in m? Assume that the returning water does not fall back on top of the jet.