232 



bubbles Increases steadily from an initial value of zero. If p, is less than 

 p^, however, a certain volume of space is freed at once by compression of the 

 water as its pressure rises from p^ to p^ . The general formula for rj at any 

 point in the cavitated region at time t is (2) 



V ~ 5 — 



1 - 



r Idv,, dv^ ^^«\ J 



[^] 



where t ^^ is the time at which cavitation occurred at this particular point 

 and v^^, v^y, and i;„ are the components of the particle velocity Vc in the 

 directions of the x, y, and z axes. Apparently, if p^^ is less than p^, t] may 

 either increase or decrease, or neither, after the breaking-front has passed. 



THE CAVITATION BOUNDARY 



When the boundary of the cavitated region, advancing as a breaking- 

 front, arrives at a point beyond which V^ as given by Equation [2] would be 

 less than the speed of sound, c, the analysis shows that it must halt abrupt- 

 ly. This may be regarded as happening either because the liquid ahead of the 

 front is not expanding with sufficient rapidity, that is, the numerator in 

 Equation [2] is too small, or because an excessive pressure gradient has been 

 encountered, that is, the denominator is too large. The boundary may then do 

 either of two things. Which it will do is found to depend in part upon the 

 particle velocity in the neighboring cavitated region, but in larger degree 

 upon conditions in the adjacent unbroken liquid. 



One alternative is that the boundary may stand still as a stationary 

 boundary, as shown in Figure 2, where any waves of pressure that may be inci- 

 dent upon it from the unbroken side are reflected as if from a free surface. 

 This must occur whenever the incident waves are very weak. 



The other alternative is that destruction of the cavitation may be- 

 gin, that is, the boundary may recede toward the cavitated region, leaving 

 the liquid unbroken again behind it. Such a boundary may be called a closing- 

 front. Apparently it may be of either of two dis- 

 tinct types. p = p_. 



CLOSING-FRONTS 



Closing of the cavitation may result from 

 a contracting motion in the cavitated region itself, 

 when the distribution of the values of v, at differ- 

 ent points are such that the bubbles tend to decrease 

 in size. This can happen, however, only if p, is ^^^^^^ ^ . A Stationary 

 less than p^ ; for, as already remarked, if p^^ = p^ Boundary 



