Water flows steadily through a fire hose and nozzle. The hose diameter is \(100 \mathrm{~mm}\) and the nozzle tip is \(30 \mathrm{~mm}\) in diameter. The gauge pressure of the water in the hose is \(525 \mathrm{kPa}\) and the stream leaving the nozzle has a uniform velocity profile. The fluid exits the nozzle at a speed of \(25 \mathrm{~m} / \mathrm{s}\).

a. Find the force transmitted by the coupling between the nozzle and the hose.

b. If the nozzle were pointed so that the water shot straight up into the air, how high would the water reach?