SHOCK WAVE MEASUREMENTS 239 



P„.(lb./i„.^)=2.25XlO^(^) 



Theoretical values from calculations based on the theory of Kirkwood 

 and Bethe are plotted as the dashed curve and are seen to be in excel- 

 lent agreement with the observations. This agreement is rather better 

 than is observed for most explosives (more detailed comparisons with 

 theory are presented in section 7.4). 



' The reduced time constant d/W^'^ is plotted in Fig. 7.5 and is seen 

 to increase slowly with distance from the charge. The experimental 

 values show somewhat greater scatter than in the case of peak pressure 

 but show no systematic departures from the estimated empirical curve. 

 The dashed line predicted by the Kirkwood-Bethe theory gives sys- 

 tematically larger time constants, which are to be attributed to the 

 exponential or peak approximation, which constrains the theoretical 

 curve to exponential form. The reduced impulse, integrated to a time 

 t = 6.7^, is plotted in Fig. 7.6. The points are fitted quite well, except 

 close to the charge, by the formula: 



7(6.70) = 2.18W 



\R ) 



The theoretical results are an even better fit, as indicated by the 

 dashed line, but the agreement in absolute value is fortuitous, as the 

 experimental results were obtained by integration of the experimental 

 curve to a finite time, and the theoretical result is for integration of an 

 exponential formula to infinite time. It is interesting to note, however, 

 that the shape of the curve is so well represented by the theory. 



The energy flux density function Ef, integrated to 6.70, is plotted in 

 Fig. 7.7 and is fitted over the entire range by the relation 



Ef = 3.27Tf 



1/3 /E^^ 



The Kirkwood-Bethe theory gives the same slope of 2.12 and a constant 

 of 4.23. The excess of this slope over the value 2.00 is a result of de- 

 partures from the acoustic inverse square law, as is the difference of the 

 peak pressure slope of 1.13 from the acoustic variation as 1/R. 



The confirmation of the principle of similarity can be extended even 

 further to the magnitudes and times of occurrence of the minimum and 

 following maximum in the pressure-time curve. The plots of these 

 pressures and reduced times are omitted here for reasons of space, but 

 it is interesting to note that the pressures fall off with distance as 

 (W^'^/Ry-^'^. The exponent 1.05 is not, nor does similarity requ're it to 

 be, the same as the value 1.13 for peak pressure, and the difference is 

 understandable in view of the lower pressure level and closer approach 

 to acoustic conditions. 



