must be considered when examining the effects of scale on inception is the dynamical behav- 

 ior of the nuclei as a function of the rate of application of pressure, i.e., the pressure gradir 

 ents. Thus, in scaling experiments in which the pressures are determined by the geometrical 

 bounaary conditions, not only will the actual time of exposure to low pressures vary but also 

 the pressure gradients.* Since, in general, with geometrically similar boundaries and the 

 sam'e velocity, the pressure gradients will increase with decreasing model size, the dynamical 

 response of the nuclei will be initially retarded and the initial appearance of an observable 

 inception will be delayed in the experiment of smaller size if the properties of the liquid are 

 independent of scale, i.e., if nuclei size remains unchanged. From a most elementary view- 

 point* it would appear, therefore, that in order to carry out experiments at reduced scale, the 

 nuclei size must vary inversely with the model scale, i.e., in order for the nuclei to grow to 

 an "observable" size (visual, aural, etc.), larger nuclei must be present in the small scale 

 experiment than in the prototype experiment. This discussion has assumed that surface .ten- 

 sion effects are always important in the inception of cavitation. If the nuclei are initially so 

 large that surface tension is not important in determining the rate of growth, then the effects 

 of pressure gradients will not be controlling and only the time of exposure need be considered. 

 However, if one further considers that only certain nuclei will grow to observable size, then 

 the number of exposed nuclei must also be considered. Thus, on a reduced scale, the tota,l 

 number of nuclei in the liquid must be greater for the smaller scale than the larger since the 

 region of low pressure is also reduced. For such considerations, the total number of nuclei 

 must vary inversely as the cube of the linear ratio.** 



The experiments on the effects of geometrical scale on cavitation inception carried out 

 at the California Institute of Technology are of particular interest in relation to the foregoing 

 remarks. It will be observed that in the type of systems investigated in these experiments it 

 was not possible to scale nuclei size and content to correspond to model scaling. 



Kermeen^^ has conducted a large number of experiments on bodies of revolution with 

 hemispherical noses and cylindrical afterbodies having diameters ranging from 1/4 to 2 inches. 

 He has observed a definite dependence of the cavitation number for inception on the model 

 size and upon the absolute flow velocity. Furthermore, as will be seen from his results, 

 Figure 2, the data cannot be correlated on the basis of Reynolds number alone. Further 

 studies have been conducted on hydrofoils by Parkin who also attempted an analysis of the 

 observations based on the growth of nuclei assumed to be stabilized on solid particles in the 

 fluid. 12 



The results shown in Figure 2, which is only a sample of the data obtained by Kermeen, 

 represent average values of a large number of data. The methods used in obtaining these data 



♦Effects of viscosity, diffusion, etc. , have been neglected in this discussion. 

 ♦♦Investigations of the various factors discussed in the foregoing are now getting underway at the Taylor Model 



