Answer to Question #238129 in Molecular Physics | Thermodynamics for Unknown346307

Question

Air at a pressure of 220 kN/m2 and temperature 27°C is moving at a

velocity of 200 m/s. Calculate the stagnation pressure if

(i) Compressibility is neglected ;

(ii) Compressibility is accounted for.

Answer 1

(i) The stagnation pressure is

$$\rho_0=\frac{p_0}{RT_0}=\frac{220·10^2}{287·(273+27)}=2.555\text{ kg/m}^3.\\\space\\ p_s=p_0+\frac{\rho_0V_0^2}{2}=220·10^3+\frac{2.555·200^2}{2}=271100\text{ Pa}.$$

(ii) Tp find the stagnation pressure in this case, first, we need to find Mach number:

$$M_0=\frac{V_0}{\sqrt{\gamma RT}}=0.576;\\\space\\ p_s=p_0+\frac{\rho_0V_0^2}{2}\bigg(1+\frac{M_0^2}{4}+\frac{2-\gamma}{24}M_0^4\bigg)=275470\text{ Pa}.$$