24 



= 16 



g 12 























/ 























/ 





















*'A 























































































































































































Frame Speed 24.6 frames 

 sec 













































































4 6 8 



Number of Frames 



Figure 3 - Typical Curves of Displacement as a Function of Time 



equivalent radius. Allen's data for bubbles greater than 0.01 cm are in- 

 cluded. The correction for wall effect has been applied to these data. 



As previously pointed out, a more generally applicable presentation 

 is that showing the drag coefficient as a function of Reynolds number with the 

 third parameter M in Equation [5] kept constant. The corresponding curve for 

 rigid spheres 12 is also included in Figure 5- 



Since it is difficult to visualize the bubble size from the value of 

 the Reynolds number, the relation between bubble size and Reynolds number for 

 bubbles rising at their terminal velocity in water is given in Figure 6. 



Examination of Figure 5 shows that up to a Reynolds number of 70> 

 the bubble behaves like a rigid sphere. For a Reynolds number range from 70 

 to 400, the bubble, althougn still spherical, has a drag coefficient consider- 

 ably less than rigid spheres. A possible explanation for the decreased drag 

 coefficient is the development of slip at the boundary of the fluid sphere. 11 

 Beyond a Reynolds number of 400, the hydrodynamic and surface-tension forces 



