Check My Solution for Second Problem (w,q)

[Kolin101]

Homework Statement

In the turbine steam changes its specific enthalpy and velocity from (3450) kJ/kg and 85 m/s at the inlet to (2630) kJ/kg and 190 m/s at the outlet. (A) Determine the power generated per 1 kg of the steam if the process is adiabatic. (B) Determine also the power generated if the heat lost to surroundings is 10kJ per 1kg of steam flowing through the turbine. Neglect change in potential energy.

Relevant Equations

Balance of Energy

Hi there again. I have a second problem for which I don't have an answer to compare with, hence I'm kindly asking someone to check the solution of mine. lower case w and q are the work and heat per 1kg respectively, and w's with a vector are of course the velocities at the inlet and at the outlet.

 

[Lnewqban]

Your work is very difficult to read, but it seems correct to my old eyes.
You are considering the simultaneous changes in kinetic energy and in thermal energy for conditions A and B.

Please, see:
https://www.power-eng.com/om/a-tale-of-two-laws-basics-of-steam-generation-thermodynamics/#gref