Question $1($Ans: $5\mathrm{.}85$ kW $)$

Lubricating oil with a specific gravity of $0\mathrm{.}9$ and viscosity of $0\mathrm{.}05$ Pa$.$s is pumped at a rate of $20\frac{L}{s}$ to a ventilated tank at a pressure of $50$ kPa gage. The increase in elevation is $6$ m $.$ The pump has an efficiency of $72\%.$ The system consists of a pump that draws the oil through an $8$ cm diameter suction and discharges through a $5$ cm diameter pipe. It is estimated that due to friction in the pipe, there are energy losses equal to $\frac{2V_p^2}{2g}$ where $V_p$ is the velocity of oil in the pipe. Determine the input power to the pump.