$=26\mathrm{.}3$ slug $\frac{?}{t^3}$; see notes at the end of the exam$)$

Oustion $2$: $(32$ points$)$

A water pumping system is used to fill a tank on a hill from a nearby lake $($water density$=1000k\frac{g}{m^3}).$ The elevation difference between the lake surface $($Point $1-$ atmospheric conditions$)$ and the water discharge point $($Point $2-$ atmospheric conditions$)$ is $25$ m $,$ as shown in the schematic. The system:

Delivers $0\mathrm{.}05\frac{m^3}{s}$ of water.

Consumes $30$ kW of electrical power.

Has a total head loss of $2$ m for the pipeline segments combined.

Has a constant pipe diameter throughout.

Calculate $($a$)$ the efficiency of the pump$-$motor assembly; and $($b$)$ the pressure drop across the pump $($i$.$e$.$ between the pump inlet and exit$).$

Free$-$body diagrams

Control$-$volume diagrams

Bernoulli's Equation points of interest

Work$-$Energy Equation points of interest

Units for all answers

Work for all calculations used in equations

Boxing$-$in$/$circling answers

Reference$/$Datum lines