Gas turbine engines provide thrust for aircraft engines and supply shaft power for various applications. They consist of three main components. That is, a compressor followed by a combustion chamber (burner) and a turbine. Both turbine and compressor components are either axial or centrifugal (radial) in design. The combustion chamber is stationary on the engine casing. The type of engine that is of interest here is the gas turbine auxiliary power unit (APU). A typical APU has a centrifugal compressor, burner and an axial turbine. APUs generate mechanical shaft power to drive equipments such as small generators and hydraulic pumps. In airplanes, they provide cabin pressurization and ventilation. They can also supply electrical power to certain airplane systems such as navigation. In comparison to thrust engines, APUs are usually much smaller in design. The purpose of this research was to investigate the possibility of combining the three components of an APU into a single centrifugal rotor. To do this, a set of equations were chosen that would describe the new turbomachinery cycle. They either were provided or derived using quasi-one-dimensional compressible flow equations. A MathCAD program developed for the analysis obtained best design points for various cases with the help of an optimizer called Model Center. These results were then compared to current machine specifications (gas turbine engine, gasoline and diesel generators). The result of interest was maximum specific power takeoff. The results showed high specific powers in the event there was no restriction to the material and did not exhaust at atmospheric pressure. This caused the rotor to become very large and have a disk thickness that was unrealistic. With the restrictions fully in place, they severely limited the performance of the rotor. Sample rotor shapes showed all of them to have unusual designs. They had a combination of unreasonable blade height variations and very large disk thicknesses. Indications from this study showed that the single radial rotor turbomachinery design might not be a good idea. Recommendations for continuation of research include secondary flow consideration, blade height constraints and extending the flow geometry to include the axial direction. / Master of Science