Do all the calculations for the following problem and show all of the steps. In the reservoir pipe system in the figure, the water sent from reservoir I to reservoir II by gravity is pumped to reservoirs III and IV by the pump placed at point B$.$The water surface elevations of reservoirs I, II and IV are $84$m$,79$m and $99$m$,$respectively$.$The energy level at point E is given as $109$m$.$Valve I is fully open at the outlet of chamber, and the valve loss coefficient will will be $=5.$

$$a$)$Determine the flow rate passing through ALL of the pipes

b$)$Find the energy height and power that the pump must give to the system. $($Efficiency coefficient $=0\mathrm{.}75)$

c$)$Draw the relative energy line of the entire system. Local head losses will be taken into account only between chambers I and II$.($Local head losses will be neglected in other sections$)$

d$)$Determine the hydraulic behavior of the pipe in the E $$IV pipe, considering that the roughness of the pipe is ks $=9\mathrm{.}10^-4$m$.$

e$)$Calculate the friction coefficient f in the square$-$section E$-$III pipe, considering that ks $=0\mathrm{.}002$m$,$using the MOODY diagram. Determine the water surface elevation of the III chamber.