420 - 6 - 



^. The relationship between the volume and the rate of rise of a bubble . 



If all the bubbles were geometrically similar and if the drag co-efficient were independent of 

 Reynolds number, it would be expected that the velocity of rise would be independent of the density 

 of the liquid and would be proportional to (volume) '. Figures 6 and 7 show the results of experiments, 

 involving 13 bubbles rising in nitrobenzene and about 75 bubbles rising in water, which were carried out 

 to test the truth of this prediction. In Figure 6, the velocity of rise, U, (in cm. /sec.) is plotted 

 against the volume, V, (in c.c.) whilst, in Figure 7, the ratio u/V^'* is plotted as a function of v^''. 

 In the diagrams, the results for t<ubbles in water and in nitrobenzene are plotted as circular dots and 

 crosses surrounded by circles respectively; the two diagrams also shew the curves derived from the 

 experimental results of Miyagi and of Moefer, 



Figure 7 shows a considerable scatter of the experimental points around the horizontal straight 

 line of ordinate li £ which represents the mean value of U/V derived from the observations; in 

 the same way, the experimental points are widely scattered araund the curve u = Zh.a V in Figure 6. 

 It is worth noticing that in Figure 7, there is no systematic variation of [1/^ with V, and that the 

 points for bubbles in water and in nitrobenzene can be represented by the same curve; in all 

 probability, the scatter cf the points is;3ue to the reasjn already put forward to account for the 

 discrepancies in Figure 5, namely the lack of geometrical similarity in the bubbles. 



4. The time of rise of gas from a deep submarine explosion . 



Photographs of bubbles produced by a spark* show that such bubbles pulsate violently and rise 

 at a very variable spee'l during the first few pulsations. The amplitude of these pulsations dies down 

 very greatly after three or four cycles and the rate of rise becomes more nearly constant, and, at the 

 same time, the bubbles assume a mushroom-like form which is rather similar to that shown in Figure 1 for 

 air released non-explosively. 



Measurements of the time-interval between the appearance of the spray dome and that of the plume 

 have been made for depth charges filled with 300 lbs. of amatol, fired at different depths. The results 

 show considerable scatter. The mean curve representing these experimental results, is shown in Figure 

 8 of the present report. It will be seen that the mean rate of rise of gas from the depth charge is 

 very rapid (of order U5 ft. /sec.) when the depth of the charge is less than about 90 feet; when the 

 charge is deeper than 90 feet, the mean rate of rise rapidly decreases. From the sound-ranging 

 observations it appears that the plume comes through the surface during the fourth oscillation if the 

 depth is about 90 feet and that bubble oscillations can hardly be distinguished beyond this point. 



It is not possible from these observations to deduce the rate of rise of gas after the bubble 

 oscillations have ceased. If, however, the rate of rise during the first four pulsations is assumed 

 to be independent of depth, the slope of the curve of Figure 8 for times greater than 2i seconds would 

 give the rate of rise after the fourth pulsation. with this assumption, the time for the gas to rise 

 from 90 feet above the charge to 13U feet above it would be 3.0 seconds, corresponding with a mean 

 velocity of 4U/3.O = in. 7 ft. /sec. |f the time from 110 to 13U feet above the charge were taken from 

 Figure 8 as 2.2 seconds, the corresponding mean velocity is 2U/2.2 = 10.9 ft. /sec. 



Taking the amount of gas released from i gm. of amatol, after the water vapour has been 

 condensed, as 650 c.c. the volume released from a 300 lb. depth charge is 8.8 x 10' c.c. The formula. 

 U = aiJ.S v'- deduced from the present experiments would therefore predict that the rate of rise of gas 

 from a 300 lb. depth charge would be 



U = 2«.8 X (8.8 X 10')'''* = 525 cm./sec. = 17.2 ft. /sec. 



For comparison with the experimental results, a straight line whose slope corresponds with this velocity 

 is shown in Figure 8. It will- be seen th=vt the actual vertical velocity of gas "from an explosion, when 



Taylor, G. I. and Davies, R.M. "The motion and shape of the hullow produced by an 

 explosion in a 1 iquid. 



