Answer
a) $\dot{V}_1=0.3079\ m³/s$
b) $\dot{m}=0.7318\ kg/s$
c) $\dot{V}_2=0.3654\ m³/s$, $\nu_2=5.94\ m/s$
Work Step by Step
At the inlet:
$\dot{V}_1=A_c\nu_1=\frac{\pi}{4} D^2\nu_1$
With $D=0.28m,\ \nu_1=5\ m/s$
$\dot{V}_1=0.3079\ m³/s$
$\dot{m}=\rho_1\dot{V}_1=\frac{P_1}{RT_1}\dot{V}_1$
With $P_1=200\ kPa, R= 0.287\ kJ/kg.K,\ T_1=293\ K$:
$\dot{m}=0.7318\ kg/s$
At the outlet:
$\dot{m}=\rho_2\dot{V}_2=\frac{P_2}{RT_2}\dot{V}_2$
With $P_2=180\ kPa,\ T_2=313\ K$:
$\dot{V}_2=0.3654\ m³/s$
$\dot{V}_2=A_c\nu_2=\frac{\pi}{4} D^2\nu_2$
$\nu_2=5.94\ m/s$
