$(30$ pts $).$ Air enters a horizontal pipe of diameter $25$ cm at a pressure of $2$ MPa $,$ a temperature of $350$ K $,$ and a velocity of $20\frac{m}{s}.$ It exits the pipe at a pressure of $1\mathrm{.}8$ MPa $,$ a temperature of $320$ K $,$ and a velocity of $18\frac{m}{s}.$ A small fan inside the pipe is spun by the flowing air and produces an output power of $2\mathrm{.}0$ kW $,$ while heat leaves the pipe. Find the heat transfer rate in kW and the mass flow rate in $k\frac{g}{s}.$ Assume the air can be treated as an ideal gas with $R=287\frac{J}{kg-K}.$ For maximum credit, start with the governing equations for open flow systems and show how this simplifies to arrive at your final numerical answer. HINT: Use Table A$-17.$