Answer
$\dot{m}=0.3674\ kg/s$
$\mathcal{V}_2=10.8\ m/s$
Work Step by Step
From table A-6:
Inlet ($P_1=1.2\ MPa, T_1=250°C$): $v_1=0.19241\ m³/kg,\ h_1=2935.6\ kJ/kg$
Outlet ($P_2=1\ MPa, h_2=h_1$): $v_2=0.23099\ m³/kg$
The mass flowrate is given by:
$\dot{m}=\dfrac{A\mathcal{V}}{v}$
Given $A_1=\dfrac{\pi D_1^2}4,\ D_1=0.15\ m,\ \mathcal{V}_1=4\ m/s$:
$\dot{m}=0.3674\ kg/s$
At the outlet $D_2=0.1\ m$:
$\mathcal{V}_2=10.8\ m/s$