15 



where N is Avogadro's number. Assuming for the fracture pressure that pres- 

 sure which gives one bubble in t seconds, i.e., -rr = -r> ^ he following pressure 

 is found upon integration: 



i6n r 3 i 1/2 



*] 



kTln NkT t/h - 4f 



Values of the fracture pressure p. corresponding to a number of waiting times 

 and several values of At * indicate insignificant differences for rather large 

 waiting periods. For computations of the rupture pressure, Fisher states that 

 the free energy of activation away from or toward a surface may be estimated 

 from the free energy of activation for viscosity since the two should be ap- 

 proximately equal. However, since computations of this quantity for viscosity 

 indicate that the value lies between and 5000 cal./mole for most liquids at 

 room temperature, 25 the error in putting 4f * = gives a value of p. "gener- 

 ally less than 5 percent and almost certainly less than 10 percent too small 

 for room-temperature liquids." Thus, Fisher finally obtains the result (with 

 t = 1 , Af Q * = 0): 



ri6rr _i 

 1 3 



kT In Nk T/h 



For water, this gives a value of -1320 atmospheres at 300° K, which, although 

 still greater than observed results, is an order of magnitude lower than the 

 value predicted on the basis of molecular forces. Fisher has carried the com- 

 putation further to investigate the formation of cavities at liquid -solid 

 interfaces, and shows that much lower tensions are required for rupture. 



Although the free energy is proportional to the viscosity of the 

 liquid', Fisher found that the pressure for rupture did not vary significantly 

 with this quantity and so neglected it in his numerical computations. On the 

 other hand, Zeldovich 30 found that the rate of formation is determined by the 

 viscosity, but that it is not important for water and gives values somewhat 

 higher than Fisher. That the breaking strength does vary with viscosity was 

 demonstrated by Briggs, Johnson, and Mason. 31 For the range of variation of 

 the viscosity of water, however, this variation in strength may be neglected. 



The details of the theory leading to the above results are beyond 

 the intended scope of this survey. However, despite the fact that the results 

 were carried out for liquids at rest and are still of little value for engi- 

 neering use, they have been included to illustrate a type of analysis which 

 may eventually lead to more precise estimates of the pressures for cavitation 

 in flowing liquids. Although, as pointed out above, the assumption that cavi- 

 tation begins at the vapor pressure corresponding to the temperature of the 



