279 



This criterion gives larger values for the critical raOius than would the criterion o' 

 Table 3a, so the smaller sizes of aiaphragm gauge are proBably safe from cavitation. The 

 « inches diaphragm gauge appears to De a borderline case according to all three criteria, and a 

 theoretical interpretation of the results is therefore likely to Be difficult. 



The Tables are set out in slightly different ways because:- 



The cri terion /^ = 1 is independent of thickness of platt, but depends on radius of 

 plate and size of charge. 



The criterion /3= a is independent of size of charge. But depends on radius and 

 thickness of plate. 



The criterion /3 = "^p'^la"- 'l ) ''^psnds on radius and thickness of plate, and also 

 logarithmically on size of charge. 



It will be noticed that none of the criteria depend on the maximum pressure. This would 

 only come in if cavitation occurred at a finite tension. 



Discussion. 



We ray therefore be confident that cavitation will occur with all the gauges of box model 

 type, and probably also with ship's plates, and with the 12 inches copper diaphragm gauge. It 

 shoula be safe to apply incompressible theory to gauges of the 'crusher' type and to the smaller 

 types of diaphragm gauge, but the 6 inches type appears to be a Borderline case from the point of 

 view Both of failure of incompressible theory and of possible cavitation. There seems to be no 

 a priori reason why one should get such a result as this, as the occurence of negative pressures 

 (leading to cavitation) and the loss of energy by radiation (leading to the failure of incompressible 

 theory) are physically quite aistinct phenomena. 



It will probably be safe to neglect the possibility of a small amount of cavitation at the 

 centre when discussing the 6 inches diaphragm gauge, but it Is very difficult to see hew to deal 

 with a case In which cavitation is occurring at the centre and over an appreciable fraction of 

 the plate, while diffraction occurs at the edge. A perhaps easier proBlem, now under 

 investigation, is to determine at what stage th^; theory of I applicable to Infinite plates breaks 

 down for finite plates. Cavitation and follow-up will now be the main effects, the diffraction 

 wave at the edges necessitating a correction, the order of magnitude of which will have to be 

 worked out . 



The results we have obtained should be compared with those of Friedlander (8), who 

 considered an infinite plate divided up into a "chess-board" by immobile stiffeners, each 'square' 

 of the chess-bo»rd being constrained to move according to the parabolic law. Now, In our first 

 two models, we found that relative t j the Infinite plate cavitation effect was hastened at the 

 central point, whereas Friedlander (8) found that cavitation, reckoned as the instant at which 

 the mean pressure over the plate dropped to zero, was later for his model than for the infinite 

 plate. If we had based our own criteria on mean pressure rather than on pressure at the central 

 point, we should, from equations (i) and (17), have deduced exactly the Taylor cavitation time 

 for Both 'piston" and "paraboloid" models, subject to the correction for the effect of the 

 alffraction wave, which can only be In the direction of Increasing mean pressure and so postponing 

 the time at which it drops to zero. There is therefore no conflict with Friedlander's work. 

 We have already pointed out that the effect of the diffraction wave In hastening cavitation at 

 the centre is a consequence of the artificial assumption of "proportional motion", which probably 

 does not represent the facts. The problem of finding a more representative model Is now under 

 invest igat ion. 



Cone Lusions and action recommended. 



(a) The best criterion for deciding whether or not cavitation occurs at a finite plate is 



probably that of Kirkwood (the Taylor cavitation time must be equal to i.) 



M 



