Aturbine rotor is designed with a free vortex distribution for both the inlet and exit flow. station 1 is the rotor inlet and station 2 is the rotor exit. the blade height is 100 mm, and the hub radius is 200 mm. the inlet conditions at the hub are: α1h = 70°, u1h = 200 m/s, and v1h = 450 m/s. the specific work extracted on the mean streamline is 100 kj/kg. simple stage assumptions apply.

find:

a) calculate the hub, meanline (50% span), and tip velocity triangles at the inlet of the rotor using an isre analysis. provide a sketch of the velocity triangles and a table of all velocities (u, v, and w) and angles (α and β).
b) calculate the hub, meanline (50% span), and tip velocity triangles at the exit of the rotor. provide a sketch of the velocity triangles and a table of all velocities (u, v, and w) and angles (α and β).
c) calculate the degree of reaction at the hub, meanline, and tip using the simple stage expression for the degree of reaction in a turbine stage: where the sign convention for the angles is given as ‘positive in the direction of rotor rotation’.
d) where does the lowest degree of reaction occur? what is a reasonable limit for the minimum degree of reaction in a turbine? why?