17 



3.0 



2.0 



1.0 



o ._ 



^^o^"-" o ~~° 



o 



0.1 



0.2 0.3 0.4 



Equivalent Radius in centimeters 



0.5 



0.6 



Figure 11 - Effect of Bubble Size on the Shape of 

 Ellipsoidal Air Bubbles Rising in Water 



Typical Shape for Spherical Cap Bubble 



4.0 



:2.0 



l.O 





































' 





e 







a 



b 





r* 





■» 













i 





9 



































6 







a 











R 



re 





^r 



° 



o 



- o^ 





o 















































• 













• 



* 





* ° 





• 



o 





o 





o 



































1.4 1.8 2.2 2.6 3.0 



Equivalent Radius in centimeters 



Figure 12 - Effect of Bubble Size on the Shape of 

 Spherical Cap Air Bubbles Rising in Water 



80 



to : 



40 



3.4 



the construction because the base of the bubble is not plane but is concave 

 downward as is indicated by the dotted line. This shape was observed by study- 

 ing the bubble from below through the transparent wall of the tank. 



Taylor and Davies considered also the shape of the bubble as related 

 to the pressure distribution over the surface. By assuming that the pressure 

 distribution for a spherical cap with a radius of curvature R is the same as 

 that of a sphere with the same radius, they show that a velocity of rise 

 2/3 VgR would result in the hydrostatic and dynamic pressure gradients nearly 

 canceling in the region around the nose of the cap. This is the required con- 

 dition along the surface of the bubble if surface tension is neglected. Their 



