358 



SECONDARY PRESSURE WAVES 



points and solid line. If the calculated pressure is plotted without cor- 

 rection for the propagation time, the lower dashed curve is obtained. 



The pressures which would exist if the initially exponential decay 

 continued are indicated by the dotted line on the semilogarithmic plot 

 in Fig. 9.1. It is evident that the noncompressive result is qualitatively 

 of the form necessary to account for the shock wave tail, and the am- 

 biguity of the calculation is suggested by the difference of the two 



3000 



1000 



CD 



liJ 

 q: 

 3 300 



(/) 



LU 

 (T 

 Q. 



100 



30 



3.0 35 



TIMt AFTER DETONATION (MSEC) 



4.0 



Fig. 9.1 Pressures in later portions of a shock wave compared with values 

 calculated from the noncompressive approximation. 



plotted curves. The result is further inaccurate because the internal 

 energy of the explosion products was neglected in the derivation of Eqs. 

 (9.7), (9.8). The effect of gas pressure has been taken into account by 

 Taylor in calculations based on numerical integration of the energy 

 equation (Eq. 8.23) backward to zero time. This leads to somewhat 

 higher pressures in the water and to the paradoxical result that the 

 minimum radius is attained at a negative time. Difficulties of this 

 kind are, as Taylor remarks, inevitable in such a calculation, for the 

 reason that the initial shock wave is taken into account only by the 

 energy Y remaining after its emission. Because of this inadequac}^ and 

 the related difficulty of the propagation time, attempts to patch to- 

 gether shock wave and noncompressive solutions, as suggested by the 

 curves of Fig. 9.1, are clearly makeshifts to avoid the formidable diffi- 



