Problem $3(34$ points$)$

A $60-$mm$-$diameter hose is attached to the discharge of a pump rated for $22\mathrm{.}5$ m of head $(\backslash ($ h$\_\{\backslash$text $\{$pump $\}\}\backslash )).$ This pump is mounted on the exterior frame of a Coast Guard rescue vessel for the purpose of fighting fires. The nozzle attached to the end of the hose has a diameter opening of $30$ mm $.$ As shown in the figure below the nozzle is located $3$ meters above the water level. Given the above information, answer the following questions.

$-$ Determine the volumetric flowrate of water through the nozzle.

$-$ Calculate the $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ reaction forces resulting from water being discharged from the nozzle at an angle of $20$ degrees as shown in the figure.

$-$ If discharge angle is changed to $90$ degrees $($i$.$e the nozzle is pointing straight up$)$ calculate the maximum height to which the water will rise.

zzle diameter opening