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It is common for centrifugal compressors to have a pressure ratio of one stage of 3, while axial compressors often have compression ratio per stage of around 1.25. What is the source of that difference in performance? Is it because the air nearer the axis of rotation in an axial compressor is slower, while in a centrifugal compressor all of the air has to pass through the high speed tips of the vanes?

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This is because of the large change in radius in a centrifugal impeller. The change in radius equates to a change in rotational speed at different radii. If you look at the Euler work equation you can see the rotational speed is a contributor to the work (slide 5 https://www.slideshare.net/toroiaritonang/pengetahuan-tentang-sentrifugal). The change in radius across an axial compressor stage is much less, therefore, not contributing to the work as much.

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