Q$3(40$pts$)$ A pump and a turbine are used in the water transmission system shown in the figure. The power required by the pump is $58kW,$ the pump efficiency is $70\%,$ and the turbine extracts $11kW$ from the flow with an efficiency of $100\%.$ The total loss between locations A and $C$ is $3$ times the velocity head at Section C$.$ The velocity in the $25cm$ diameter pipe section is $5\frac{m}{s}.$

a$)$ Find the elevation at $C$ that the water can be raised by the pump.

b$)$ Compute the pressures at points $B$ and $E,$ if the head loss between A and $B$ is equal to the velocity head at Section $C($no head loss between $B$ and E$).$

c$)$ Compute the horizontal and vertical reaction forces on the support of the pump.

d$)$ Draw the energy and the hydraulic grade lines on the figure.