A blade pair in an axial flow compressor is being designed. The axial flow component of gas velocity is $183\frac{m}{s}.$ The engine diameter at the mean blade height is $0\mathrm{.}83m$ and the blade height at rotor inlet is $0\mathrm{.}16m.$ The rotor absolute inlet flow angle is $26$ degrees. The stagnation conditions at the inlet to the blade pair are $297K$ and $132k\frac{N}{m^2}.$

Using $Cp=1\mathrm{.}005k\frac{J}{k}\frac{g}{K},R=0\mathrm{.}287k\frac{J}{k}\frac{g}{K},$ and taking the ratio of specific heat capacities as $1\mathrm{.}4,$ calculate the engine mass flow rate to the nearest $k\frac{g}{s}.$