$4($b$)\_$#$3$: Air from the surrounding atmosphere at $100$kPa,$20C,$ enters a compressor with a velocity of $8\mathrm{.}6\frac{m}{s}$ through an inlet whose diameter is $36$ cm $.$ The compressed air exits at $650$ kPa,$225C,$ with a velocity of $2\mathrm{.}8\frac{m}{s}.$ The rate of entropy generation for the compressor is $0\mathrm{.}062k\frac{W}{K}.$ Determine the power input to the compressor, $($in$))$