Answer
$\dot{W}_{flow}=0\ kW$
Work Step by Step
From table A-12:
Inlet ($P_1=320\ kPa=P_2=P_3, x_1=0.55$): $v_1=0.03537\ m³/kg,\ v_G=v_2=0.06368\ m³/kg,\ v_L=v_3=0.0007771\ m³/kg$
$\dot{m}=\dot{V}/v,\ \dot{V}_1=0.006\ m³/s$
$\dot{m}_1=0.1696\ kg/s$
$\dot{m}_2=x_1\dot{m}_1=0.09329\ kg/s$
$\dot{m}_3=(1-x_1)\dot{m}_1=0.07633\ kg/s$
$\dot{W}_{flow}=\dot{m}_2P_2v_2+\dot{m}_3P_3v_3-\dot{m}_1P_1v_1$
$\dot{W}_{flow}=0\ kW$
