Question 8.1: We are to design a supersonic wind tunnel using a large vacu......
We are to design a supersonic wind tunnel using a large vacuum pump to draw air from the ambient atmosphere into our tunnel, as shown in Fig. 8.4. The air is continuously accelerated as it flows through a convergent/divergent nozzle so that flow in the test section is supersonic. If the ambient air is at the standard sea-level conditions, what is the maximum velocity that we can attain in the test section?
To calculate this maximum velocity, all we need is the energy equation for asteady, one-dimensional, adiabatic flow. Using equation (8.29), we have
h_1+\frac{1}{2} U_1^2=h_2+\frac{1}{2} U_2^2
Since the ambient air (i.e., that which serves as the tunnel’s “stagnation chamber” or “reservoir”) is at rest, U_1=0. The maximum velocity in the test section occurs when h_2=0 (i.e., when the flow expands until the static temperature in the test section is zero).
\begin{gathered} (1004.7) 288.15 \mathrm{~J} / \mathrm{kg}=\frac{U_2^2}{2} \\ U_2=760.9 \mathrm{~m} / \mathrm{s} \end{gathered}
Of course, we realize that this limit is physically unattainable, since the gas would liquefy first. However, it does represent an upper limit for conceptual considerations.