time following detonation. According to his theoretical predictions in first paper [4]
we have seen from Eq. (5.24) that the radius of the shock front has the following
time-dependence (with γ ¼ 1.4);
R t
ð Þ ¼ 1:033
E 0
ρ 0
1=5
t
2=5 ,
hence,
R t
ð Þ
ð
Þ
5=2 ¼ 1:033
ð
Þ
5=2 E 0
ρ 0
1=2
t:
By taking logs to the base 10 of this latter equation, we can write it as,
5
2
log 10 R ¼ log 10 t þ log 10 1:033
ð
Þ
5=2 E 0
ρ 0
1=2
"
#
:
Fig. 5.10 A plot showing the fraction of the energy used for propagating the blast wave when the
shock front has expanded to a radius where the blast pressure (in atmospheres) is y 1 (γ ¼ 1.4)
250
5 Spherical Shock Waves: The Self-similar Solution
we have seen from Eq. (5.24) that the radius of the shock front has the following
time-dependence (with γ ¼ 1.4);
R t
ð Þ ¼ 1:033
E 0
ρ 0
1=5
t
2=5 ,
hence,
R t
ð Þ
ð
Þ
5=2 ¼ 1:033
ð
Þ
5=2 E 0
ρ 0
1=2
t:
By taking logs to the base 10 of this latter equation, we can write it as,
5
2
log 10 R ¼ log 10 t þ log 10 1:033
ð
Þ
5=2 E 0
ρ 0
1=2
"
#
:
Fig. 5.10 A plot showing the fraction of the energy used for propagating the blast wave when the
shock front has expanded to a radius where the blast pressure (in atmospheres) is y 1 (γ ¼ 1.4)
250
5 Spherical Shock Waves: The Self-similar Solution