48 



In discussing the collapse phases, care must be taken to distinguish 

 the "type" of cavitation under consideration. There is much discussion in the 

 literature of the pressures developed by a single "transient cavity" (see, 

 e.g., References 12, 31, 46, k~J , 50, 75, ~[6) and of a mass of such bubbles, 10, 

 and 75- However, the writer has found no parallel analysis for the collapse 

 of the large steady-state cavities corresponding to the observed- oscillations 

 of such cavities in the MIT venturi studies 59 and in the DTMB results men- 

 tioned in the foregoing. Descriptions of the motion and, consequently, the 

 collapse process in such cavities have been proposed herein in the previous 

 discussion. 



ARGUMENTS FOR THE MECHANICAL ORIGIN OP DAMAGE 



In the case of the small, transient cavities, collapse begins upon 

 entrance to a high pressure region. For the Rayleigh (empty) cavity, the mo- 

 tion is governed by the inertial effects of the liquid and the ambient pres- 

 sures. In Plesset's extension, the additional effect of "surface tension" is 

 included but he did not compute collapse pressures. Rayleigh' s computation 50 

 gives for the velocity of the cavity wall, 



&i&'^ 



'-T-J-P. 



where R Q is the initial cavity radius, and R the radius corresponding to U. 

 The pressure in the vicinity of the cavity has a maximum at 1-57 R from the 

 center equal to 



It is clear that the pressure may rise indefinitely depending on the radius 

 of the cavity. Assuming that the cavity collapses concentrically onto a rig- 

 id sphere and that the kinetic energy of the fluid is converted into elastic 

 energy of compression, Cook (see Rayleigh ' s paper) found for the pressure 



p-vfW 7 ^) 



R 



where k is the volume modulus of compressibility. 



Rayleigh extended the computation for the case of isothermal com- 

 pression of a permanent gas in the cavity, and showed that the cavity oscil- 

 lates between the initial radius R and a limiting radius which may be ob- 

 tained from the equation 



