Consider the Euler turbine equation for a system with a root diameter of $0\mathrm{.}9$ m and an edge diameter of $1\mathrm{.}8$ m$.$ The inlet temperature of steam is $1454$ degree C for a rotating system at $800$ rpm$.$ The axial velocity of the system is $7$ m$/$s with inlet guide vanes turning by only $20$ degrees.

Consider the angles present at the root and tip of the first stage of the turbine. Consider some options:

Turn the amount the same at both location $($consistent shape turbine$)$

Similar torque system with a $15\%$ increase at the edge

Produce an analysis of geometries that would drive the torque produced by the steam.

Report on the complexities of the shape factor of what you are proposing and whether its effectiveness warrants the complexity of the design.