Design a natural gas power engine which can provide 1MW power output. In the design, you have to provide us the pressure ratio, inlet/outlet diameters of the compressor and turbine in the final answer. The required stoichiometric air-fuel ratio and heating value of natural gas can be found through google searches. Your power engine should be as small as possible as well as satisfying the following constraints :

(a) The maximum pressure of your natural gas power engine should not be higher than 10% of the fatigue limit of steel

(b) The maximum temperature of your power engine should not higher than 1000 K

(c) The fluid velocity should not be higher than 50% of the sound speed.