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I'm currenty doing a course in trubomachinery at the university were I've got stuck on the following question:

An axial turbine has a reaction ratio $R =\frac{1}{2}.$ Air enters the rotor with relative velocity at an angle $β_2 = 15^\circ$, and the axial velocity is constant for the stage. The blade speed is U = 300 m/s, and the tangential velocity change across the rotor is $V_{u2} − V_{u3} = 320 m/s.$

Were I need to find:
(a) Find the axial velocity.
(b). Find the angle at which the absolute velocity enters the rotor.

I've done the following: My solution p.1

My solution p.2

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