Hydroelectric Power Station $(25$ marks$)$

Draw a schematic diagram of the hydroelectric power station shown in Fig. $3$ and clearly label all nodes and elements in your diagram. Construct a linear graph representation for the hydroelectric power station. A river supplies the reservoir and is modelled as a flow source. The pipe is long and relatively small in diameter, and the turbine$/$generator is to be modelled by a D$-$Type element.

$($a$)$ Derive the elemental equation for the reservoir assuming it is a linear element and indicate how a numerical value for the element parameter might be obtained. Is it reasonable to expect the element to be linear? Why or why not?

$($b$)$ Do the same for all elements associated with the long pipe.

Figure $3$: Hydroelectric power station