Problems of Chapter 9

Problem 9.1

With the relations given in Chapter 6 we find cPs = a) 1.827, b) 1.839. The closeness of the values reflects the Mach-number independence principle.

Problem 9.2

ps = a) 47.3-рж, b) 84-рж, c) 129.7-рж d) ж-рж. The pressure ps increases with increasing Mach number. It is only the pressure coefficient, which be­comes Mach-number independent. The excess pressure in the Edney type IV case is Aps = 706-рж.

Problem 9.3

We measure in Fig. 9.21 the shock angle to в « 11.8°. This gives M^N « 2.58. This is somewhat above the permissible value given in Sub-Section 6.3.3.

The flat-plate results nevertheless are acceptable, because Figs. 9.23 and 9.24 show that the Rankine-Hugoniot values are met quite well.

Problem 9.4

X = 20.77, V = 0.1296. If a hot wall is assumed, we get хсгц = 180.09 cm, with the cold wall assumption xcrit = 17.05 cm. With the total temperature being To ~ 3,500 K, the wall can be considered as cold wall. The dimensionless critical value then is xcrit (= x/Lsfr) = 2.55. Fig. 9.23 shows that for x = 2.5 the static pressure has almost attained the plateau typical for boundary-layer flow.

Problem 9.5

At x = 1 m we find x = 0.185, V = 0.004. The critical value is хсгц = 0.002 m. Strong interaction phenomena could be neglected if the lower stage of SANGER would have a sharp nose.

Problem 9.6

At x = 1 m we find x = 1-662 and V = 0.0166. хсгц = 0.173 nr. In the nose region strong interaction phenomena are to be expected.