fluid_mechanics

11.3 Categories of Compressible Flow 589
The wave pattern
from a moving
source is not
symmetrical.
number and Mach number is shown for air flow over a sphere. Compressibility effects can be of
considerable importance.
To further illustrate some curious features of compressible flow, a simplified example is considered.
Imagine the emission of weak pressure pulses from a point source. These pressure waves
are spherical and expand radially outward from the point source at the speed of sound, c. If a pressure
wave is emitted at different times, t wave , we can determine where several waves will be at a
common instant of time, t, by using the relationship
r 1t t wave 2c
where r is the radius of the sphere-shaped wave emitted at time t wave . For a stationary point
source, the symmetrical wave pattern shown in Fig. 11.3a is involved.
When the point source moves to the left with a constant velocity, V, the wave pattern is no
longer symmetrical. In Figs. 11.3b, 11.3c, and 11.3d are illustrated the wave patterns at t 3 s for
different values of V. Also shown with a “ ” are the positions of the moving point source at values
of time, t, equal to 0 s, 1 s, 2 s, and 3 s. Knowing where the point source has been at different
instances is important because it indicates to us where the different waves originated.
From the pressure wave patterns of Fig. 11.3, we can draw some useful conclusions. Before
doing this we should recognize that if instead of moving the point source to the left, we held the
point source stationary and moved the fluid to the right with velocity V, the resulting pressure wave
patterns would be identical to those indicated in Fig. 11.3.
c
2c
3c
3c
2c
c
V
2V
3V
(a)
(b)
Zone of silence
Zone of action
Tangent plane
(Mach wave)
c
2c
3c
Zone of silence
α
c
2c
3c
2V = 2c
3V = 3c
V = c
Mach cone
Zone of action
(c)
Wave emitted at t = 0 s Wave emitted at t = 1 s Wave emitted at t = 2 s
Source at t = 0 s
3V
(d)
Source at t = 1, 2, or 3 s
F I G U R E 11.3 (a) Pressure waves at t 3 s, V 0; (b) pressure waves at t 3 s,
V 6 c; (c) pressure waves at t 3 s, V c; (d) pressure waves at t 3 s, V 7 c.
2V
V