-5- 419 



The accuracy of the relationship (2.6) can be judged from Figure i», in which the values of u 

 given in taOle I are plotted against the values of/sT it will bt- seen that the experimental points 

 are, on the whole, reasonably well represented by the straight line given by the relationship u = 2/3 



/gR. 



The values of Cq given in table I are very variable and they do not appear to show any consistent 



variation with respect to either of the variables a. or Re. At an early stage in the experiments it 



was thought that c^ might be a function of tc and, for comparison, a series of experiments was carried 



out in a wind-tunnel in order to find how the drag co-efficient of a rigid spherical cap varied with the 



semi-vertical angle <^^. The cap was supported so as to face the wind and Its leewacd side was closed 



with a plane metal disc; using pressure orifices connected in turn to a manometer, the pressures at 



various points on the curved and flat surfaces of the cap were determined and the drag co-efficient 



calculated in the usual way'. Four Dodic-s, with ». radius of 1 inch and with CD equal to 90°, 75°. 



' m ^ 

 55 and 30 respectively were used In the experiments and the values cf c. are given in the second column 



of table II. In the experiments, the wind speed was kept constant at 1500 cm. /sec, and the values of 



the Reynolds numbers, defined by equation (2.8) are given in the third column of the table. 



Drag CO - e fficients of a rt^id spherical ca p . 



These value cf Cq plotted against cz.^, are shown in Figure 5 by the circular dots; this diagram 

 also shows the values of Cr. given in table I for bubbles rising in nitrobenzene. 



It is clear that, wnereas the results of the wind-tunnel experimrnts lie on a smooth curve, the 

 results of the nitrobenzene experiments shew ; rathrr l?,rge scatter, and, in addition, the goneral trend 

 of the curve of closest fit drawn through the points for the bubbles (indicated by the broken line in 

 Figure 5) differs considerably from the curve- jiven by the wind-tunnel txpt;riments. 



It is difficult to be certain of the re-aion for th.-se effects. They may, for ex=imple, oe due 

 to the variation in Reynolds number, =.lthouah this is unlikely since the values of C. for the bubble show 

 no systematic variation with Reynolds number. it is more likely that the effects in question are due to 

 variations in the shape of the bubbles. In this connection, it must be remembrred that our photographs 

 show only the projection of a bubble on a vertical plane, so that the lower surface of a bubble Is 

 invisible unless it is convex downards. Visual observation shows that the lower surface is, in fact, 

 usually concave downards, its curvature being less than that of the upper surface, and the difference 

 between the observed (Cp, 0,^^) curves for the oubble and for the wind-tunnel experiment may be caused by 

 the difference in the wa«e in the two experiments, due to the difference In the geoinetrical forms of the 

 bubble and the flat-bottomed spherical cap. 



Similarly, in the case of the bubbles themselves, the scatter of the experimental values of C^ 

 for a given value cf <p^ nay be caused by differences in the valu" of the ratio of the curvatures of the 

 upper and lower surfaces when <^ is constant 



See for example. R. jones, Phil. Trans. A Vol. 226 p. 231, (l927). 



