EML 4711/5710 Gas Dynamics 12/9/02
Closed notes Van Dommelen 5:30-7:30 pm

(1) The book, a calculator, and MathCad with Charney's formulae may be used. (2) Show all reasoning and intermediate results leading to your answer, or credit will be lost. (3) Where tables are used, list table and column number. (4) Unless otherwise noted, the gas is air, R = 287 m²/sec² K = 1716 ft²/sec² R. (5) You must use only the unit system (SI or British) used in the question to answer them. 1 BTU = 778 ft lbf, 1 slug = 32.2 lbm. (6) Standard sea level conditions are p = 101,325 Pa = 2116 lbf/ft², T = 288 K = 518.4 R.

1.

Design the windtunnel sketched below to operate at a Mach number 2.9 in the measurement section, which should have a 1 ft² cross section. The stagnation temperature completely upstream is 300 K at all times. The exit area should also be 1 ft²; it is at atmospheric pressure. Ignore the effects of any oblique shocks. Find:

(a)

Static air temperature in the measurement section.

(b)

Upstream throat area.

(c)

Optimum diffuser throat area.

(d)

Minimum upstream stagnation pressure required to start the tunnel.

(e)

Upstream stagnation pressure at which the tunnel unstarts.

(f)

Diffuser efficiency at the unstarting pressure.

Solution. Gaseqs log.

2.

The shock tube with the x,t-diagram below has an initial air temperature of 300 K, and the initial pressure is 4 atm to the left of the membrane and 1 atm to the right of it. Neatly and accurately draw both u and a versus x for the time corresponding to the grey line A-F in the x,t-diagram. Identify all the u and a values occurring in the two graphs. Also find u and a behind the reflected shock and behind the reflected expansion wave.

Solution. Gaseqs log.