50 



the Clapeyron equation for equilibrium between liquid and vapor phases.* Sup- 

 posing, then, that the total energy (surface and gas) is given up to the liq- 

 uid as potential energy of compression, Silver found for the maximum pressure 



,/^f^hfn} 



where k is the bulk modulus of the liquid , 



V and V are the specific volume of vapor and liquid, respectively, and 

 y is the surface tension. 



Assuming further that the pressure is propagated as a spherical wave (i.e., 

 varies inversely with the distance from the source), Silver computes the pres- 

 sure which would be produced at a solid surface by a bubble which is initially 

 tangent to this surface and obtains the result 



Ps = W;) m 



In spite of the objection that can be raised that Silver did not take into 

 account the effect of wall proximity, the result is of interest in that it 

 shows that the pressure pulse of a single bubble touching a surface cannot be 

 less than 1 / kp(V s /V w ) 1/3 . Silver extended the computation for a mass of bub- 

 bles, but the above result is sufficient to show the order of magnitude of 

 the pressures. Where the Rayleigh theory including surface tension (worked 

 out by Beeching 76 ) gives pressures of the order of hundreds of tons per 

 square inch, Silver's result predicts pressures of the order of tens of tons, 

 which are of the proper order for fatigue failure of cast metals. 



The preceding results have been presented as indications that the 

 pressures developed at collapse of isolated cavities are sufficient to account 

 for cavitation damage. On the other hand, a rather interesting hypothesis was 

 outlined by Poulter 77 in 194-2, in which he attributed damage to pressure' re- 

 lease rather than pressure application. In a series of experiments on glass 

 and quartz rods, Poulter showed that breakage would occur on release of pres- 

 sure slowly applied through several different liquids, and that the suscepti- 

 bility to breakage increased with increased time of pressure application. 

 Also, since the specimens were found to withstand greater pressures with oil 

 or glycerine as compared with water, alcohol or ether, Poulter concluded that 



*A further objection to Silver's analysis is that he used differences rather than complete partial 

 differential equations. However, judging from a similar computation made by the writer, 4 Silver's 

 results are probably not too greatly in error. 



