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The design process begins with the construction of velocity triangles.

Flow Direction: Parallel to the axis of rotation.

In 2021, the demand for higher thermal efficiency, driven by climate change mandates and fuel cost volatility, has necessitated a re-evaluation of conventional design limits. While axial turbines dominate the high-power sector due to their ability to handle large volumetric flows with high efficiency, radial turbines maintain a monopoly in small-scale applications where compactness and robustness against particle ingestion are paramount. This paper delineates the theoretical framework required to design and analyze these machines, providing engineers with the necessary tools to navigate the trade-offs between complexity, cost, and performance.