As problems 5.18 and 5.19 reflect, the air temperature in the test section of conventional hypersonic wind tunnels is low. In reality, air liquefies at a temperature of about \(50 \mathrm{~K}\) (depending in part on the local pressure as well). In the practical operation of a hypersonic wind tunnel, liquefaction of the test stream gas should be avoided; when liquefaction occurs, the test stream is a two-phase flow, and the test data is compromised. For a Mach 20 tunnel using air, calculate the minimum reservoir temperature required to avoid liquefaction in the test section.

Data From Problem 5.19:

Consider a hypersonic wind tunnel with a reservoir temperature of \(3000 \mathrm{~K}\) in air. Calculate the theoretical maximum velocity obtainable in the test section. Compare this result with the results of problem 5.18 (a) and (b).

Data From Problem 5.18:

Consider two hypersonic wind tunnels with the same reservoir temperature of \(3000 \mathrm{~K}\) in air.

(a) One tunnel has a test-section Mach number of 10. Calculate the flow velocity in the test section.

(b) The other tunnel has a test-section Mach number of 20. Calculate the flow velocity in the test section.