$2)$ An expansion engine can be modeled as a chamber in which $2$ flows of water mix and one resulting flow leaves, while producing power $($see diagram below$).$ In this problem, $2$ kg$/$s of water at $2000$ kPa and $520$C mix with $480$ g$/$s of water at $125$ kPa and $30$C$.$ The exit flow has a quality of $80\%,$ a pressure of $150$ kPa, and a diameter of $15$ cm$.$ There is a heat loss equivalent to $300$ kW$.$ Find: a$.$ The volume flow rate of the two inlet flows$$ b$.$ The velocity of the exit flow$$ c$.$ The power produced by the engine$$ d$.$ List all assumptions $($make sure u answer all parts, list all states, list all interpolations if any, all tables used, all diagrams drawn for a thumbs up$)$