$1.$ Problem $5\mathrm{.}109$ in book $($modified$).$ A pump with certain power, of dimensions $\backslash (\backslash$frac$\{$F L$\}\{$T$\}\backslash ),$ is to move water from a lake into a large pressurized tank, with pressure P $,$ as shown in the figure.

$($a$)$ Draw the energy grade line and the hydraulic grade line connecting the water level at the lake and the water level at the pressurized tank. Assume that the reservoir and the tank are large enough so the water level remains the same.

$($b$)$ What is the minimum head that the pump has to add to the system in order to move the water from the lake to the tank? Express the pump head as a function of elevation, pressure, velocity and loss heads. If any of the components is zero, state it in the problem solution.

$($c$)$ If the pump will move the water at a volumetric flow rate Q $,$ what is the minimum power of the pump $($Work per time$)$ required for the system to work?