14 



Equivalent 

 Radius, cm 



0.055 



0.073 



0.159 



Reynolds 

 Number 



237 



448 



850 



Scale 



1.29/1 



1-37/1 



0.528/1 



Time Inter- 

 val, sec 



0.0185 



0.0407 



O.0588 





• 





• 

 • 



• 

 • 



• 



• 



m 

 m 



Figure 7 ~ Photographs Showing the Shape and Paths of 

 Typical Bubbles for Reynolds Numbers less than 1100 



equivalent radius of 0.35 cm. Beyond this size, the ratio remains the same 

 but the shape of the bubble becomes increasingly irregular. Finally, at a 

 value of r greater than 0.55 cm, the shape varies so greatly, as the bubble 

 rises, that no specific values of a/b can be assigned. The transition to 

 spherical caps is completed at an equivalent radiuf of 1.0 cm. The shape of 

 a spherical cap can be adequately described in terms of the radius of cur- 

 vature R of the nose, the transverse dimension a of the bubble, the height 

 b of the bubble, and the angle subtended <f>. The angle <f> and the ratios R/r e 

 and a/b for a number of representative bubbles are shown as a function of 

 bubble size in Figure 12. Although the scatter is considerable, the data show 

 that all three parameters are independent of the bubble size, with a/b about 

 4.02, R/r about 2.5, and <f> approximately 50 degrees. 



