$12.[15]$ Consider the pump storage system shown at the right.

The surface water of the two large reservoirs has an elevation difference of $200$ m and $\backslash (\backslash$mathrm$\{$T$\}=20\backslash$mathrm$\{$C$\}\backslash ).$ The pipe is a commercial steel pipe $(\backslash (\backslash$varepsilon$=\mathrm{.}045\backslash$mathrm$\{$~mm$\}\backslash ))$; it has a $0\mathrm{.}1$ m diameter and the total pipe length is $300$ m $.$ Determine the pump power required $\backslash ((\backslash$mathrm$\{$W$\})\backslash )$ following the steps below, if the pump delivers $\backslash (0\mathrm{.}01\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($a$)$ Define a control volume for the problem by labeling its inlet and exit in the figure.

$($b$)$ Specify the shaft head and pump power required assuming no losses.

$($c$)$ Repeat $($b$)$ accounting for major losses.

$($a$)$ From top of lower reservoir to top of upper reservoir.

$($b$)200$ m and $19600$ W

$($c$)203$ m and $19900$ W