230 



scattered through the water. Such bubbles have often been observed, but in 

 many cases they seem to contain air In addition to water vapor, and they do 

 not always disappear when the pressure Is raised. All such complications 

 will be ignored here, however, in order to obtain a tractable analytical the- 

 ory. The bubbles may be supposed to be so small that the resulting Inhorao- 

 geneity of the water may be neglected; and p^ may be supposed to equal the 

 vapor pressure of the water. 



The discussion will be limited to motion that is Irrotational or 

 free from vortices, m.otion such as can be produced by the action of pressure 

 upon frlctionless liquid. Furthermore, all variations of pressure will be 

 assumed to be small enough so that the usual theory of sound waves is appli- 

 cable to the unbroken water; but no limit need be set upon the magnicude of 

 Its particle velocity. 



BREAKING-FRONTS 



Cavitation will begin, according to the assumptions just made, in 

 a region where the pressure is falling, and at a point of minimum pressure, 

 at the instant at which the pressure sinks to p^^ . A cavity will form and 

 this cavity, for reasons lying outside the assumptior^s of the analytical the- 

 ory, will at once become subdivided into bubbles. Since, however, the pres- 

 sure will be sinking in the neighboring water also, the same process will 

 soon occur at neighboring points as well. 

 Thus a cavitated region will form, sur- 

 rounding the point of Initiation. The 

 boundary of this region will sweep out 

 into the unbroken water as a breaking- 

 front, Figure 1 . Since the pressure 

 gradient at the Initial point of mini- 

 mum pressure is zero, the velocity of 

 advance of the breaking-front is seen 

 to be Infinite at first. Just as, when 

 a rounded bowl is lowered into water, 

 the boundary of the wetted region moves 

 out at first at infinite speed. Hence 



cavitation occurs almost simultaneously throughout a considerable volume, re- 

 sulting in a fairly uniform distribution of bubbles; there is no reason to 

 expect the immediate formation of a large cavity anywhere. 



The speed of propagation of the breaking-front relative to the wa- 

 ter ahead of it, Vj, can be shown never to sink beiow the speed of sound, c. 

 Usually Vj is greater than c. This means that no influence can be propagated 



Figure 1 - An Expanding Breaking- 

 Front, where p = p,^. Surrounding 

 a Cavitated Region 



