Question #238129

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.


1
Expert's answer
2021-09-17T09:23:27-0400

(i) The stagnation pressure is


ρ0=p0RT0=220102287(273+27)=2.555 kg/m3. ps=p0+ρ0V022=220103+2.55520022=271100 Pa.\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:

M0=V0γRT=0.576; ps=p0+ρ0V022(1+M024+2γ24M04)=275470 Pa.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}.


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