1. (4 points) A helicopter gas turbine requires an overall compressor pressure ratio of 10: 1. This is to be obtained using a two-spool layout consisting of a four-stage axial compressor followed by a single-stage centrifugal compressor. The polytropic efficiency of the axial compressor is 92 percent and that of the centrifugal is 83 percent. The axial compressor has a stage temperature rise of 30 K, using a 50 percent reaction design with a stator outlet angle of 20°. If the mean diameter of each stage is 25.0 cm and each stage is identical (assume inlet guide vanes are present to give the required pre-whirl), calculate the required rotational speed. Assume a work-done factor of 0.86 and a constant axial velocity of 150 m/s. Assuming an axial velocity at the eye of the impeller, an impeller tip diameter of 33.0 cm, a slip factor of 0.90 and a power input factor of 1.04, calculate the rotational speed for the centrifugal compressor. Ambient conditions are 1.01 bar and 288 K.