Johnson and Hsieh 



intersection of the R*^ and R*p curves, therefore, gives the value of vapor 

 cavitation number, for which there is only one size of bubble which can possibly 

 become unstable in the flow field for the specific body size, speed, and entrained 

 bubble population which includes all sizes, < r; < * . Let this bubble size be 

 defined as Rq j . That is, for a slight increase of the vapor cavitation number (an 

 increase of the free stream pressure) all bubble sizes will remain stable. On 

 the other hand, for a slight decrease of the vapor cavitation number, additional 

 sizes of bubbles will become unstable. Thus, the value of the vapor cavitation 

 number at the intersection of the R*^ and R*^ curves is the incipient cavitation 

 number 7^. Consequently, a curve of incipient cavitation number versus body 

 size can be deduced from the results presented in Fig. 7 and this curve (labeled 

 5 Rq < °°) is shown in Fig. 8. In Fig. 8 the dashed curves present the com- 

 puted values of y.^ obtained when the bubble population in the oncoming stream 

 is void of bubbles below a specified size. It is interesting to note that the body 

 size effect becomes more and more significant as the value of the minimum 

 bubble radii in the bubble population is increased. 



Another interesting point to note is that in Fig. 8 for each specific body 

 size, the R^^^ and Rg^ form an envelope of an unstable bubble zone. It is seen 

 that to have "minimum scale effect, we need the bubble with radii Rqj to be 

 present in the entrained bubble population. Furthermore, for a range of en- 

 trained bubble population of radius greater than Rq ■ , it is always the smallest 



0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 



HALF ULTIMATE BODY WIDTH- h, INCHES 



4.0 6.0 8.0 10.0 



Fig. 8 - The effect of body size on the inception of cavitation 

 as a function of minimum radius of gas nuclei (U = 50 fps) 



176 



