experiments with spherical-cap bubbles in nitrobenzene showed excellent agree- 

 ment with their theory. This was also done at the Taylor Model Basin and the 

 results are shown in Figure 13. It can be seen that the observed rates of 

 rise are equal to about 0.645 f'gR rather than 2/3 V'gl. This indicates that 

 the dynamic-pressure gradient along the bubble surface is somewhat greater 

 than the one computed for a sphere of the same nose radius. 



90 













































« 









v = 3^R-\ 





6 









\ 



^ 



y 



c 

















z> 

















'o 



S 50 

 « 



> 



£ 









ff 



'jr 















TMB Dat<A 

 O 







S* O 



''IS' 



o 











3 4 5 



Radius of Curvature R in centimeters 



Figure 13 - The Terminal Velocity of Spherical Caps as a Function 

 of the Radius of Curvature of the Nose of the Bubble 



SIGNIFICANCE OF THE PARAMETER M 



Since the TMB experiments were all conducted in water at one temper- 

 ature, only the bubble size being varied independently, no information concern- 

 ing the effect of the parameter M can be derived from these data. This param- 

 eter was, in fact, chosen so as to be independent of the variables in the ex- 

 periments. It may be varied independently of the Reynolds number by changing 

 either the pressure gradient or the properties of the liquid. In connection 

 with the study of bubble motion in water, the effect of varying pressure gra- 

 dients is directly of interest. Unfortunately, no data are available concern- 

 ing the behavior of bubbles in water at pressure gradients other than that pro- 

 duced by gravity. Some measurements have been made, however, to determine the 



