15 



Equivalent 

 Radius, cm 



0.322 



0.808 



1.76 



Reynolds 

 Number 



1460 



4570 



13,790 



Scale 



0.522/1 



0.382/1 



0-375/1 



Time Inter- 

 val, sec 



0.0588 



0.0633 



0.0643 



Figure 8 - Photographs Showing the Shape and Paths of 

 Typical Bubbles for Reynolds Numbers Greater than 1100 



SPHERICAL CAPS 



Taylor and Davies 17 made extensive Investigations of bubbles having 

 the shape of spherical caps. They suggest that the drag coefficient and shape 

 of spherical-cap bubbles are independent of the Reynolds number. Their em- 

 pirical relation between the rate of rise and bubble size provides a value of 

 2.6 for the drag coefficient which is in complete agreement with the TMB ex- 

 perimental results shown in Figure 5. The results of a number of measurements 

 of selected bubble dimensions presented in Figure 12 likewise agree with their 

 conclusion regarding the geometric similarity of spherical caps of various 

 sizes. 



By using the experimental values of the subtended angle and the 

 ratio a/b,-a somewhat idealized picture of a representative bubble can be con- 

 structed as is shown in Figure 12. The value for R/r cannot be utilized in 



