Solution Guide and Solutions of the Problems

Problems of Chapter 2

Problem 2.1

The nominal density at 70 km altitude is рж = pnom = 8.283-10-5 kg/m3, Table 2.1. The actual density is pactuai = 7.4Б47-10-5 kg/m3.

Assume that the RV can be approximated by a flat plate and determine the drag with the help of Newton’s theory, Section 6.7:

CD = 2 sin3 a.

This relation yields

CDnom = 0.707.

Because the actual drag is to be the nominal one, we have pnomCDnom = pactUaiCDcorr. We obtain from this CDcorr = 0.78Б.

Make a Taylor expansion around the actual drag coefficient and keep the linear term only:

+ O(Aa2)).

From that equation the correction angle Aa is found to be

, dCD m

da

With

dCD
2.1213 rad-1,
da

the correction angle is Aa = 0.037 rad, respectively Aa = 2.12°.

With the corrected angle acorr = 47.12° the value CDcorr = 0.787 is obtained.

(C Springer International Publishing Switzerland 2015 E. H. Hirschel, Basics of Aerothermodynamics,

DOI: 10.1007/978-3-319-14373-6 _11

Problem 2.2

Remember the mass fractions of the undisturbed air and find eventually with eq. (2.6): a) pn2 = 912.98 Pa, po2 = 284.05 Pa, b) pn2 = 0.803 Pa, po2 = 0.250 Pa.

Problem 2.3

Determine the density in the test section, take the simple approximation for the viscosity of air, Section 4.2, p = 0.702-10-7 T, find A facility = 0.00003 m, and Dfacility = 0.0001 m.