P$.1$ Consider a pump that runs $12$ hours$/$day$,5$ days$/$week for $50$ weeks per year. Measurements

show a pressure rise of $250$ kPa across the pump and flow rate of $0\mathrm{.}1\frac{m^3}{s}.$ The system has a motor

with $80\%$ efficiency, a drive with $95\%$ efficiency, and pump efficiency of $70\%.$ With proposed

improvements, the pressure rise will be reduced to $200$ kPa at the same flow rate. Also, the motor

will be replaced with a high efficiency one with $93\%$ efficiency. The new operating point of the

pump has $80\%$ efficiency. Calculate:

Energy savings $($ kWh $)$

Demand savings $($kW$-$months$)$

Cost savings for the proposed changes $($ $ $).$ Assume $$\frac{0\mathrm{.}15}{k}Wh$ cost of electricity and

$$\frac{20}{k}W-$month for demand.

P$.2$ Consider a piping system as shown in the diagram below where water at $15C$ is pumped

through steel pipes with $100$ mm internal diameter.

a$)$ Derive and plot the system equation, $H=f(A{A}^{}),$ for this piping system, where $H$ is head in

meters and $A{A}^{}$ is volumetric flow rate in $\frac{m^3}{m}in.$

b$)$ Assuming velocity at point $C$ is $2\mathrm{.}5\frac{m}{s},$ and gauge pressure at points $B$ and $C$ are $125$ kPa

and $175$ kPa $,$ respectively, calculate the water horsepower for the pump.