Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

858 | Thermodynamics

FIGURE 17–47

The complex interactions between
shock waves and expansion waves in
an “overexpanded” supersonic jet.
The flow is visualized by a schlieren-
like differential interferogram.

Photo by H. Oertel sen. Reproduced by courtesy of
the French-German Research Institute of Saint-
Louis, ISL. Used with permission.

EXAMPLE 17–10 Estimation of the Mach Number

from Mach Lines

Estimate the Mach number of the free-stream flow upstream of the space

shuttle in Fig. 17–36 from the figure alone. Compare with the known value

of Mach number provided in the figure caption.

Solution We are to estimate the Mach number from a figure and compare

it to the known value.

Analysis Using a protractor, we measure the angle of the Mach lines in the

free-stream flow: m
19°. The Mach number is obtained from Eq. 17–47,

Our estimated Mach number agrees with the experimental value of 3.0 
0.1.

Discussion The result is independent of the fluid properties.

msin^1 a

1

Ma 1

b S Ma 1 

1

sin 19°

S Ma 1 3.07

EXAMPLE 17–11 Oblique Shock Calculations

Supersonic air at Ma 1 2.0 and 75.0 kPa impinges on a two-dimensional

wedge of half-angle d  10° (Fig. 17–48). Calculate the two possible

oblique shock angles, bweakand bstrong, that could be formed by this wedge.

For each case, calculate the pressure and Mach number downstream of the

oblique shock, compare, and discuss.

Solution We are to calculate the shock angle, Mach number, and pressure

downstream of the weak and strong oblique shocks formed by a two-

dimensional wedge.

Assumptions 1 The flow is steady. 2 The boundary layer on the wedge is

very thin.

Properties The fluid is air with k1.4.

Ma 1

Strong

shock

d  10 °

bstrong

(a)

(b)

Ma 1

Weak

shock

d  10 °

bweak

FIGURE 17–48

Two possible oblique shock angles,
(a)bweakand (b) bstrong, formed by a
two-dimensional wedge of half-angle
d 10 .