- 9 - 



277 



to point definitely towards the second assumption, in that, to obtain agreement we have to 

 use the Taylor cavitation time instead of the shorter time predicted for a rigid piston, 

 but more work will be needed before this conclusion can be said to be finally established. 

 In the reantime it is 'air to point out that the fact that plastic waves cannot travel as 

 fast as sound waves in water is one that is physically established, whereas the assumption of 

 •proportional motion" was a pur.?ly artificial one, introduced in order to simplify the 

 mathematics. This assumption is probably quite good enough for the purpose of determining the 

 final deflection of the plate with reasonable accuracy, but the notion of the central point 

 during the early motion will not be given correctly, and requires more elaborate investigation. 



Criteria for the validity of Incompressible Theory, and for the occurrence 

 o f Cavitation, applied to various Gauges , 



The situation is now as follows. Inspection of equations (8) and (l8) indicates that 

 incompressible theory is likely to bcome a poor approximation if the non-dimensional quantity 

 /3 is of the order of unity or greater. The assumption that the plate moves like a rigid 

 piston suggests that cavitation is likely to set in if a is of the order of nnagnitude of /3 

 or less. The alternative and physically more plausible assumption introduced suggests that 

 cavitation will set in if j = ^ log (u) or greater, that is 1^ = "■ M . °- . it is 



Important to examine how nearly these criteria are satisfied for gauges and models used In 

 practice. We have three variables, size of charge, unsupported area of plate (expressed by 

 means of the radius of a circle of equal area) and thickness of plate. 



TABLE 2 

 Criterion US = i) for failure of incompressible theory, assuming no cavitation . 



Thus, it is clear that, quite apart from any question of cavltati n, we could not hope 

 to interpret the deflections of gauges of the box model type by means of incompressible theory, 

 though it should be quite satisfactory for the smaller sizes of diaphragm gauge, and even more 

 so for gauges of the "crusher" type, where the exposed area of piston Is very snail. Border- 

 line cases are the 12 inches and 6 inches diaphragm gauges, where /? would not be snail compared 

 with unity for the smaller charges. (it is proposed to apply the corrected form of 

 incompressible theory to the 6 inches diaphragm gauge, In order to examine this point more 

 closely). 



Table 3a. 



