Shock 
front 
351 
=~ 5 — 
A check on Kirkwood's theory of the propagation of the pressure pulse in water has been 
made by Road Research Laboratory by comparing the time and space derivatives of the pressure just 
behind the shock-front, as it can be shavn that these are connected by a unique relation. It 
reveals discrepancies of up to 30% in the values obtained from Kirkwood's assumptions in the very 
high pressure region occurring initially near the charge. Tnis check is a sensitive one, and does 
not imply that values of peak pressure, etc., show errors of this order. 
The extrapolation process. 
As stated, the step-by-step process was used until the shock-front had reached a point about 
5 — 6 charge radii from the centre, and the pressure had dropped from its original high value of the 
order of 40 kilobars to about 2 kilobars. Some specimen values of P and Q and the pressure are 
given in Table Il, 
TABLE II]. 
Values after the final step. 
T.N.T./ Aluminium 
Q 
cms. kilobars metres/sec.| metres/ 
sec. 
Shock 
front 
Inter— 
face 
Original radius of charge was 50 cms. in both cases. 
It will be seen that, even at these comparatively low pressures, the function Q is stil) not 
negligible except in the region just behind the shock-front. An attempt to carry the step-by-step 
process further (we need values at least 10 charge radii to get a satisfactory comparison with 
experiment) might lead to an unacceptable piling up of errors, while any extrapolation process 
involves the neglect of the ingoing wave. It was considered, however, that the application of such 
a process would give a better answer than either further application of the step-by-step method or 
Kirkwood's method, which amounts virtually to an application of extrapolation starting from an 
instant just after the pressure-pulse has begun to form, In particular, it should give a sufficiently 
good answer for the variation of peak pressure at various positions of the shock-front, and for the 
portion of the pressure—time curve immediately behind the shock-front. On the assumption that Q is 
zero, we have:— 
Ugh es (3) 
Also P= f+u (25) = ¢+ a from equation (1). 
35 
Therefore .sar5 
