10 



237 



where L is any convenient linear dimension. It is clear that L, like v^ , 

 must be kept constant. Thus, if cavitation within the midst of a liquid is 

 accompanied by the formation of cavities of considerable size, no transfor- 

 mation of similarity is possible at all. 



The inclusion of effects of viscosity, on the other hand, requiring 



preservation of the quantity 



pvL 



V 



where v is the viscosity, is known to destroy the possibility of similarity, 

 irrespective of whether cavitation occurs or not. 



In experiments such as those on cavitating propellers, transforma- 

 tions of similarity can be made for two reasons. In the first place, the 

 compressibility of the water can be neglected, as well as the viscosity ef- 

 fects, so that only two quantities need to be preserved in value, such as 



V 9^ 



In the second place, only a single cavitation pressure is usually recognized, 

 and this can be taken as the datum pressure which is held constant. The usu- 

 al change of scale then becomes possible in which all linear dimensions and 

 also the excess of pressure at each point over the cavitation pressure are 

 changed in proportion to ?;^. If, however, it became necessary to distinguish 

 between two cavitation pressures, a breaking-pressure and a cavity pressure, 

 then the fixed difference between these two would require all pressure dif- 

 ferences to be fixed, and consequently similar motions on different linear 

 scales could not occur. 



APPLICATION: CAVITATION BEHIND* A PLATE 



The simplest case to which the analytical theory of cavitation 

 can be applied is that of plane waves of pressure falling at normal inci- 

 dence upon a uniform plane sheet of solid material, where the sheet is so 

 thin that elastic propagation through its thickness need not be considered; 

 see Figure 6. 



Various aspects of this case have been discussed in several reports 

 (3) Ci) (5) (6). If the pressure wave is of limited length and of suffi- 

 ciently low Intensity to make acoustic theory applicable, and if water can 

 support the requisite tension, then it has been shown that the initial for- 

 ward acceleration of the plate is followed by a phase during which it is 

 brought to rest again by the action of tension in the water. The final dis- 

 placement of the plate is equal to twice the total displacement of a particle 



On the side acted on by the explosion. 



