(Solved): Water is pumped from a lower reservoir to a higher reservoir by a pump with a shaft power. of 30k ...

Water is pumped from a lower reservoir to a higher reservoir by a pump with a shaft power. of $30\mathrm{kW}$ and an efficiency of $75\%$. The free surface of the upper reservoir is $30\mathrm{m}$ higher than the surface of the lower reservoir. The flow rate of water is measured to be $10\mathrm{U}/\mathrm{s}$, and density of water is $1000\mathrm{kg}/{\mathrm{m}}^3$, a) Determine the irreversible loss in pipe of the system in the unit of $m$ and $\mathrm{kW}$, respectively. In order to get the full credit, draw a control volume and designate inlet and outlet regions. b) Calculate the pressure difference (i.e. Pon $?P_{in})$ across pump if the diameter of the pipe is $5\mathrm{cm}$ on the intake side and $3\mathrm{cm}$ on the discharge side. Kinetic correction factor is assumed to be one, and elevation difference between intake and discharge sides are negligible. In order to get the full credit, draw a control volume and designate inlet and outlet regions. c) Now, a motor is added to the pump, and overall efficiency of motor-pump is $65\%$. What is the electrical power applied to the system? Units: $1N=\left[\mathrm{kg}?\mathrm{m}/{\mathrm{s}}^2\right],1Pa=\frac{N}{m^2}=\left[\mathrm{kg}/\mathrm{m}?{\mathrm{s}}^2\right],1\mathrm{W}=\frac{L}{s}=\frac{\mathrm{Nm}}{\mathrm{s}}=\left[\frac{\mathrm{kgm}}{{\mathrm{s}}^2}?\frac{\mathrm{m}}{\mathrm{s}}\right],1000\mathrm{L}=1{\mathrm{m}}^3$