$7.(30$ points$)$ A pump takes water from a large tank and discharges it into the atmosphere through a horizontally$-$oriented, $25-$mm nozzle. The nozzle is $4$ meters above the water surface and is connected to the pump's $50-$cm diameter discharge pipe. In the $50-$cm diameter pipe just before the nozzle, the pressure is $276$ kPa $.$ The efficiency of the pump is $\backslash (80\backslash \%\backslash ).$

a$.(14$ pts$)$ What is the volumetric flow rate from the nozzle in $\backslash (\backslash$mathrm$\{$m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )?$

b$.(8$ pts$)$ What is the useful head of the pump in meters?

c$.(8$ pts$)$ What is the minimum power required for the pump have in kW $?$