Environmental Engineering Reference
In-Depth Information
T
:
2
¼
2
b
ð
2
:
71
Þ
The solution for above simultaneous equations is Eq.
2.72
.
a
¼
0
;
b
¼
1
;
c
¼
1
ð
2
:
72
Þ
The relations of all physical quantities are certain, which do not change after
their units vary. So the function of
D
P
;
Q
V
; q
0
;
r
;
R
;
p
a
;
and
q
a
is similar to the
function of
D
P
;
Q
V
; q
0
;
r
;
R
;
p
a
;
and
q
a
.
Q
V
; q
0
;
r
;
R
;
p
a
; q
a
D
P ¼ f
ð
Þ
ð
2
:
73
Þ
Substitute
2.66
and
2.67
into
2.73
,
Q
v
p
a
D
P
p
a
¼ f
ð
=
q
a
;
q
0
r
R
;
1
;
1
;
1
Þ
q
a
;
ð
2
:
74
Þ
In Eq.
2.74
, the three constants 1 do not have any special meaning, so the
dimensionless Eq.
2.75
is obtained.
!
Q
v
p
a
D
P
p
a
¼ f
=
q
a
;
q
0
r
R
q
a
;
ð
2
:
75
Þ
The function f is still not clear yet. Its determination needs the support of more
experiments. But Eq.
2.75
is much simpler than
2.65
. By using dimensionless
parameters, the three augments are reduced, and it decreases the experiment work.
If the experiments are condu
ct
ed under the same conditions using same explosive
with same packing density,
and
q
0
Q
v
p
a
=
q
a
q
a
are constants. Equation
2.75
is simpli
ed as
Eq.
2.76
.
D
P
p
a
¼ f
r
R
ð
2
:
76
Þ
After multiple experiment, only if
r
1
R
1
¼
r
2
R
2
¼
r
3
R
3
¼
¼
Constants
ð
2
:
77
Þ
All measured super pressure are the same, this is the explosion geometric sim-
ilarity law of air shock waves.
