Problem $\backslash$#$3(10$ points$)$

A geothermal source provides $\backslash (5\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$ of hot water at $600\backslash (\backslash$mathrm$\{$kPa$\},150^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ flowing through a throttling valve and then going into a rigid and well$-$insulated flash evaporator that separates saturated vapor and saturated liquid at $100$ kPa $.$

a$)$ Find the flow work per unit mass flow $($in $\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ))$ at the inlet $1,$ exit $2,$ and exit $3.$

b$)$ Find the enthalpy per unit mass flow $($in $\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ))$ at the inlet $1,$ exit $2,$ and exit $3.$

c$)$ Find the water mass flowrate at the exit $2$ and at exit $3.$