Question

Determine the stagnation temperature and stagnation pressure of air that is flowing through a duct at 36 kPa, 238 K, and 330 m/s.

The properties of air at room temperature are c_p = 1.005 kJ/kg·K and k = 1.4.

The stagnation temperature and stagnation pressure of air that is flowing through a duct at 36 kPa, 238 K, and 330 m/s is ? K and ? kPa, respectively.

Answer 1

Given data →

Static properties of duct are

Pressure (P) = 36 kPa

$\textup{Temperature}\left ( T \right )=238\textup{ K}$

$\textup{Velocity}\left ( V \right )=330\textup{ m/s}$

$\textup{The properties of air at room temperature are}$

$c_{p}=1.005*10^{3}\textup{ J/kgK}$

$\gamma =1.4$

Solution →

$\textup{Stagnation temperature is given by}$

$T_{o}=T+\frac{V^{2}}{2c_{p}}$

$T_{o}=238+\frac{330^{2}}{2*1.005*10^{3}}$

$T_{o}=292.179\textup{ K}$

$\textup{Stagnation pressure is given by}$

$P_{o}=P*\left ( \frac{T_{o}}{T} \right )^{\frac{\gamma }{\gamma -1}}$

$P_{o}=36*\left ( \frac{292.179}{238} \right )^{\frac{1.4}{1.4-1}}$

$P_{o}=73.799\textup{ kPa}$