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Summary, 



The probletT of detarmining the history of c=ivitation arJ follcw-up ofwater when an 

 infinite plate is subjected to an exponential underwater explosion pulse has 3e-,n considered in 

 Roport "Theoretical Investigation on Cavitation Phenomena cccurriny when an Underwater Pressure 

 Pulse is incident on a yielding surface - I." referred to as I. In the present report a start is 

 tiade on the problem of taking into account the modifications introduced if the plat-- is clamped 

 at the edges and surrounded by an infinite rigid baffle. The consequencjs of the custonary 

 assumption of "proportional motion" are worked out in two specific cases, the "rigid piston" and 

 the "paraboloid" a pproxi (rations, and it is concluded that, in both, thr c.vitation tims, 3S 

 determined by vanishing pressure at the centril point, is shartened, as compared with the infinite 

 plate, due to the effect of the diffracted iv?.ve from the ed.^e. It is founo th=t the conditions 

 at which cavitation just fails to occur also mark approximately the upper limit for the validity 

 of incompressible theory and correcting terms are worked out for sucn a case. 



The assumption of "proportional motion" is criticised on tne ground that it is probably 

 not valid during the early motion of the plate, and a more natural assumption is found to lead 

 exactly to the criterion for cavitation at a finite plate suggested by Kirkwood (6), which is 

 known to give good agreement with the experiments so far carried out.. The criteria established 

 for the occurrence of cavitation and for the failure of incompressible theory are applied to 

 various types of diaphragm gauge. It is found that aauges of tne "box model" type are so far 

 removed from the critical region that the theory of I is probably valid, and that it should be 

 fair to apply incompressible theory to gauges of the crusher type and to the smaller sizes of 

 diaphragm gauge. The 6 inch copper diaphragm gauge appears to be a borderline case, where readings 

 will be hard to interpret in terms of absolute values, though a corrected version of incompressible 

 theory may prove satisfactory. Some suggestions for further work are outlined. 



Introduct i cri .. 



In a previous report (l) referred to hereafter as I, an account has been given of the 

 present position of the theory of the motion of a clamped plate when subjected to an explosion pulse. 

 It is there shown that a plaie whose dimensions are large ccmpared with the distance sound travels 

 in the cliaracterist ic time of the assumed exponential pressure will behave very like a free surface, 

 and, in particular, that finite tensions will first occur in the water near th-j plate, and will 

 spread out into the water behind the reflected pulse. Taylor (2) solved the problem of the motnon 

 of such a plate, first on the assumption that watir can stand tension everywhere, secondly on the 

 assumption that water can stand tension, but that the- interface between water and plate cannot, so 

 that the plate leaves the water as soon as tension sets in, and acquires no further energy from it. 

 In I, the same problem was solved, in some reprssentat ive cases, on the assumption that water cannot 

 stand tension at all, so that cavitation sots in wherever the pressure in the water drops to zero. 

 The laws of the propagation of the cavitation front, and of the distribution of velocity in the 

 cavitation zone, can easily be written down, and the equations governing the motion of the plate 

 when bombardea by the cavitated water, accompanied by the disappearance o' the cavitation, can also 

 be formulated, but have to be solved numerically. It was found that the effect of the cavitated 

 water colliding with the plate, thus communicating extra energy to it, may be very important for 

 plates of thicknesses usual in ship construction, even though an appreciable percentage (of the 

 order of 30i) of the kinetic energy of the cavitated water is lost on collision with the plate. 



The modifications required by the fact that a plate may be clamped at the edges, as in a 

 diaphragm gauge, and that the clamped edges nay be surrounded by a practically rigio baffle, as in 

 the box model, or again by the fact that a plate may be backed by stiffeners, as in a ship, were 

 discussed qualitatively in I. To a first approximation, the effect of a baffle can be taken into 

 account if we regarJ the plate as a piston moving in an aperture in a rigid wall. The relationship 

 between this model and the infinite plate theory has been discussed by Butter\"crth and Wiggles'"orth 

 (3), who sho'vcd that, provided cavitation does not occur, the mot 'on of the piston could. In a 

 typical case, have been represented by incompressible theory to a good approximation. It is the 

 purpose of this report to examine this relationship a little more closely, and to try and set up a 

 criterion to determine whether tension will occur or not. If tension does not occur, then one can 

 be confident of the absence of cavitation, but if one is near the critical region it may be that 

 some correction to the result given by incompressible theory is needed. If tension docs occur, 

 then one would expect the investigation given in I for an infinite plate t'j give satisfactory 

 results provided that one were well away from the critical region, but near It one would have to 

 take account simultaneously of diffraction and cavitation which would be very difficult. In this 

 report we shall not attempt either of these last two problems. 



The 



