Environmental Engineering Reference
In-Depth Information
Fig. 2.42 Mach re
fl
ection
The properties of re
fl
ected waves are listed below.
(1) For a given strength of incident waves, there is critical angle
u
1c
,that when
u
1
[
u
1c
, there is no re
fl
ection. For air with speci
c heat ratio k ¼
1
:
4, the
90
; the limit of strong shock waves
limit of weak shock waves is
u
1c
¼
sin
1 1
97
≈
.
(2) For each gas, there is an angle
u
1c
¼
K
¼
39
:
40
°
1
2
cos
1
k
1
u
0
¼
2
u
1
[
u
0
, the intensity of re
When
fl
ected waves is larger than that of front
23
.
(3) For a given strength of incident waves, there is an incident angle
u
0
¼
re
fl
ection. For air,
39
:
u
min
. When
u
1
¼
u
min
, the re
fl
ection intensity P
2
=
P
0
has the minimum value.
(4) Re
fl
ection angle
u
2
is a monotonic increasing function of
u
1
.
(3) Mach re
ection of shock waves [
27
,
28
]
In the regular re
fl
u
1
is larger than the critical angle
fl
ection, when incident angle
u
1c
, the above re
fl
ection rule does not work. Ernst Mach indicated that the merge of
incident and re
fl
ected shock waves produces the third shock waves
—
Mach waves.
This phenomenon is Mach re
ection.
The general explosion in air occurs in a limited height. The shock waves are in
spherical shape. After transportation in air, the radius of the sphere becomes larger
gradually, and exceeds the height H. Now part shock waves run into the ground. On
the projected point of explosion center, the propagation direction of shock wave
fl
