Explosion Features of Liquid Explosive Materials - Liquid Explosives - page 88

s

1
q 0

1
q 1

# 1 # 0 ¼ ð P 1 P 0 Þ

s

1
q 1

1
q 2

# 2 # 1 ¼ ð P 2 P 1 Þ

ection waves are opposite from the incident ones, the
incident waves are positive, the re

Because the direction of re fl

fl ection waves are negative, and # 1 ¼ # 2 ¼ 0, so

1
q 0

1
q 1

1
q 1

1
q 2

ð P 1 P 0 Þ ¼ P 2 P 1 ð Þ

or

¼ P 2 P 1

P 1 P 0
q 0

q 0
q 1

q 1
q 2

1 ð Þ 1 ð 2 : 95 Þ

The adiabatic function of shock waves is below.

P 1 P 2

k þ 1 k þ 1

k 1 P 0 þ

1

k 1 P 1 þ

1

q 1
q 0 ¼

q 2
q 1 ¼

;

P 1
P 0

P 2
P 1

k þ 1 k þ 1

k 1 þ k 1 þ

Substitute the adiabatic function into Eq. 2.95

2

2 P 1 P 0 ð Þ

q 1 k ½ ð 1 Þ P 1 þ k þ ð 1 Þ P 0

2

2 P 2 P 1 ð Þ

¼

q 1 k þ ½ ð Þ P 2 þ k ð Þ P 1

1 1

2
1

¼ #

The super pressure of incident waves is

D P 1 ¼ P 1 P 0

And the super pressure of re fl ection waves is

D P 2 ¼ P 2 P 0

The above equation is changed to

2

D P 2

ð

D P 2 D P 1

Þ

2kP 0 ¼

ð k 1 Þ D P 1 þ ð k þ 1 Þ D P 2 þ k þ ð 1 Þ P 2 þ k ð 1 Þ D P 1 þ 2kP 0