485 
where 2 ~| 
fe 2Cie gst G U 
ae ss s 2_,)2 d 
(p,, Ud i £(1-9) G V> U (9.22) 
and where D(R) is given by Eq. 9.13 and ng), Mp)nave been given for the 
one~dimensional case. When b, (Rk ) is known, the profile z (if ) of the 
shock front can be obtained by an auxiliary integration 
evy2 Ne 
a» > 
We note that Lim (U,» oa) @ =1, and Bq. 9.21 is identical with Eq. 9.1, 
Z(R) = dr, (9.23) 
in this limit. Also, Lim (pv) d = 1, and the asymptotic solutions of 
Eqs. 9.14 and 9.21 have the same form. 
The two constants of integration can be determined from the thermo- 
dynamic properties of the explosive and those of its products in the Chapman- 
Jouguet detonation state or in the instantaneous detonation state. The con- 
stants of integration may be conveniently selected as k, and €, » the 
initial values of the peak pressure and the total shock-wave energy deliv— 
ered by the explosion products from unit mass of explosive. 
The initial excess pressure P, and particle velocity u, » con= 
tinuous at the boundary, are determined by the relations, 
V2 
A Os Le 
op.) = uo | Uy | ain -~ 2b f/+--=,], 
C, Q D 
p/p Ur, U= Ufa), (9.2h) 
95 
