Air at a pressure of $220 \mathrm{kN} / \mathrm{m}^{2}$ and temperature $27^{\circ} \mathrm{C}$ is moving at a velocity of $200 \mathrm{~m} / \mathrm{s}$. Calculate the stagnation pressure if,

(i) Compressibility is neglected;

(ii) Compressibility is accounted for.

For air take $R=287 \mathrm{~J} / \mathrm{kg} K, \gamma=1.4$.

Solution:

Pressure of air, $ p_{0}=200 \mathrm{kN} / \mathrm{m}^{2} \\ $

Temperature of air, $ T_{0}=27+233=300 \mathrm{~K} \\ $

Velocity of air, $ V_{0}=200 \mathrm{~m} / \mathrm{s} \\ $

Stagnation pressure, $p_{s}$ :

(i) Compressibility is neglected :

$$ p_{s}=p_{0}+\frac{\rho_{0} V_{0}^{2}}{2} \\ $$

where, $$ \rho_{0}=\frac{p_{0}}{R T_{0}}=\frac{220 \times 10^{3}}{287 \times …