Question#$1(5$ marks$)$

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides $19\mathrm{.}5$ kW of useful mechanical power to the water. The free surface of the upper reservoir is $44$ m higher than the surface of the lower reservoir. If the flow rate of water is measured to be $0\mathrm{.}03\frac{m^3}{s},$ determine the irreversible head loss of the system and the lost mechanical power during this process.

Question#$2(5$ marks$)$

A vented tanker is to be filled with fuel oil with $=920k\frac{g}{m^3}$ and $=50\mathrm{.}045k\frac{g}{m}*s$ from an underground reservoir using a $25-m-$long, $4-cm-$diameter plastic hose with a slightly rounded entrance and two $90$ smooth bends. The elevation difference between the oil level in the reservoir and the top of the tanker where the hose is discharged is $5$ m $.$ The capacity of the tanker is $18m^3$ and the filling time is $30$ min $.$ Taking the kinetic energy correction factor at the hose discharge to be $1\mathrm{.}05$ and assuming an overall pump efficiency of $82$ percent, determine the required power input to the pump.