THEORY OF THE SHOCK WAVE 133 



step-by-step process was then carried out on the basis of Eqs. (4.24) to 

 approximately 6 charge radii, at which point the shock wave pressure 

 was found to have a nearly linear decay behind the front, as shown in 

 Fig. 4.5. 



The calculated values of peak pressure Pm as a function of shock 

 front radius R agreed closely with the formula 



(4.25) Pm (lb./in.2) = 103,000 ^^ eW« 



ti 



over the range ao < R < Qao, where ao is the charge radius. The initial 

 density of the explosive was taken as 1.5 gm./cm.^ and converting Eq. 

 (4.25) to charge weight W in pounds and distance R in feet gives 



P^(lb./in.2) = 14,000^ eO.274 fi'3/72 

 R 



A detailed comparison with experiment is given in section 4.7, but it 

 may be mentioned here that the predicted pressure of 12,600 Ib./in.^ at 

 10 charge radii is 20 per cent lower than recent experimental values at 

 this distance. 



4.6. The Propagation Theory of Kirkwood and Brinkley 



An approach to the solution for shock waves of the basic hydrody- 

 namic equations has been developed by Kirkwood and Brinkley (60), 

 which is particularly convenient for extending experimentally deter- 

 mined shock wave data obtained at a single distance, or over a limited 

 range, to other distances. As has been shown, the equation of motion 

 and equation of continuity provide two partial differential equations for 

 the pressure P and particle velocity u as functions of distance r and 

 time t. In the case of spherical symmetry these equations are (see sec- 

 tion 2.3) 



<-' '(i),+'-(s)+eT),=« 



pc^ \dr )t \dr Jt r \dp ), 



If these equations are specialized to the shock front, they provide 

 two relations among the four partial derivatives of P and %i. A third 

 such relation can be obtained from the Rankine-Hugoniot condition for 

 conservation of mass at the shock front, and the other shock front con- 

 ditions permit evaluation of the shock front density and velocity as 



