Question 13.17: A jet plane is traveling at M = 1.5, where the absolute air ......
A jet plane is traveling at M = 1.5, where the absolute air pressure is 50 kPa and the temperature is 8°C. At this speed, a shock forms at the intake of the engine, as shown in Fig. 13–38a. Determine the pressure and velocity of the air just to the right of the shock.
Fluid Description. The control volume that contains the shock moves with the engine so that steady flow occurs through the open control surfaces, Fig. 13–38b. An adiabatic process occurs within the shock.
Analysis. The velocity V_2 will be obtained from V_2 = M_2 \sqrt{kRT_2}, and so we must first obtain M_2 and T_2. Since k = 1.4, using Eqs. 13–73, 13–76, and 13–69, or Table B–4, for M_1 = 1.5 (supersonic), we have
M_2 = 0.70109 Subsonic
M_2^2 = \frac{M_1^2 + \frac{2}{k – 1}}{\frac{2k}{k – 1} M_1^2 – 1} M_1 > M_2 (13-73)
\frac{p_2}{p_1}=\frac{2k}{k+1}M^2_1-\frac{k-1}{k+1} (13–76)
\frac{T_2}{T_1} = \frac{1 + \frac{k – 1}{2} M_1^2}{1 + \frac{k – 1}{2} M_2^2} (13-69)
\frac{p_2}{p_1} = 2.4583\frac{T_2}{T_1} = 1.3202
Therefore, just to the right of the shock,
p_2 = 2.4583 (50 kPa) = 123 kPa
T_2 = 1.3202(273 + 8) K = 370.98 K
Thus, relative to the engine, the velocity of the air is
V_2 = 271 m/s
