SURFACE AND OTHER EFFECTS 417 



tional to tlie impulse Pmd of the incident wave. If coo is large, one has 

 sin (VoUn = l/cood giving the result that Zc{tm) — 2Pmdp/poCo. This is just 

 the expression found by neglect of diffraction in the corresponding limit 

 of short plastic times and, as before, the deformation is determined by 

 peak pressure, as of course it must be. It is interesting to note that the 

 equation of motion and its solution are very similar to those for the 

 ball-crusher gauge (see section 5.1). 



The results of the noncompressive approximation have been extended 

 by Kirkwood to include bafRes of finite rather than infinite extent. 

 These results have been found to describe the deformations of small 

 steel diaphragms in the diaphragm gauge described in section 5.3 with 

 considerable accuracy, both as to magnitude of central deformation, and 

 its variation with charge weight and distance. The observed values 

 average some fifteen per cent lower than the calculated ones, but this 

 difference is partly removed by the use of experimental pressure-time 

 curves rather than the actually employed values from the Kirkwood- 

 Bethe shock wave theory.^ When this is considered, the agreement 

 obtained is perhaps fortuitously good, considering the many approxi- 

 mations necessary in the theory. It is to be emphasized that the theory 

 cannot always be applied this successfully, particularly if cavitation 

 occurs. 



Kirkwood and Richardson have made a number of investigations 

 aimed at removing some of the arbitrary and approximate features of 

 the simple theory which has been presented here, such as the parabolic 

 constraint, the neglect of tangential plastic waves, and other ideali- 

 zations of the plastic state. For an account of these results, reference 

 should be made to the original reports (61). 



B. The effect of cavitation on deformation. The analysis of diaphragm 

 motion which has been given assumes that the resultant pressure on the 

 surface is at all times given by superposition of the incident and dif- 

 fracted waves. In many cases, however, this resultant pressure wdll 

 become negative because of the deformation, which would require that 

 the water withstand tension if the analysis is to continue to apply. 

 Except under laboratory conditions water cannot withstand appreciable 

 tensions, as discussed in section 10.4, and when cavitation takes place 

 the results already discussed and others similarly obtained must fail. 

 Some criterion as to whether cavitation actually occurs is thus obvi- 

 ously desirable. An essential factor in considering cavitation is the 

 fact that the circumstances which lead to cavitation in front of an 

 infinite plate are modified by the equalizing effect of diffraction from 

 the edge of a finite plate. For example, the decrease in pressure by 

 acceleration at the center of the plate will be counteracted by the ar- 

 rival of diffracted waves w^hich act to equalize the pressure with the 



^ The calculations are summarized in a report by Fye and Eldridge (39) . 



