229 



In terms of a target of arbitrarily assumed properties, such as might serve 

 to measure directly the pressure in the water. 



The behavior of an acoustical wave incident on a solid or free 

 boundary in water is rather fully understood; and the shock wave radiated 

 from an explosion in water partakes in large degree of the nature of an 

 acoustical wave. Even in such waves, however, the continuity of the medium 

 is believed to be broken at times by tensile effects to which the water re- 

 sponds by cavitation. In the shock wave, where pressures are a whole order 

 higher than in an acoustical wave, cavitation naturally has that much more 

 significance. Among the problems which must be solved before interactions 

 between field and target can be subjected to study by calculation, that of 

 cavitation must rank high in importance. 



HYDRODYNAMICAL THEORY OP CAVITATION IN BULK 



In practical experience cavitation usually originates between water 

 and a solid surface, such as a propeller blade. There are some indications, 

 however, that it may also occur in the midst of a mass of water, as for ex- 

 ample when explosive pressure waves are reflected from the surface of the sea. 

 To determine the effect of such cavitation upon the motion of the water, a 

 certain extension of hydrodynamlcal theory is required. 



In the present report -the necessary extension of the theory will be 

 described, but the complete mathematical details will be published elsewhere 

 (2). The theory is based upon certain simple assumptions, which are laid 

 down without entering upon the complicated question as to the nature of the 

 cavitation process itself. Two applications of the theory will be discussed, 

 dealing respectively with the impact of a pressure wave upon a plate, page 10, 

 and upon the surface of the sea, page 19. 



The following assumptions will be made: 



(a) cavitation occurs wherever the pressure in the water sinks 

 to a fixed value p^, called the breaking-pressure; 



(b) upon the occurrence of cavitation, the pressure instantly 

 becomes equal to a fixed value p^, called the cavity pres- 

 sure, which cannot be less than p^, so that 



P,^P, [ 1 ] 



(c) when the pressure rises above p^, the cavitation disappears 

 Instantly. 



How far these assumptions correspond to the actual behavior of wa- 

 ter is not yet known. The value to be assigned to p^ is discussed briefly 

 on page 17. The cavitation will undoubtedly take the form of small bubbles 



