415 

 THE RATE OF RISE OF LARGE VOLUMES OF GAS IN WATER 

 G. I. Taylor and R. M. Davies 

 June 1944 



Summary. 



The work descrioed in this report is concerned with the rate of rise of bubbles, ranging in 

 volume from 1.5 to lOO cc, produced by the non-explosive release of a volume of air in nitrobenzene 

 or in water. 



Measurements of photographs of Bubbles formed in nitrobenzene showed that the central portion 

 of the upper surface was spherical in form. A theoretical discussion, based on the assumption that 

 the pressure over the front of the bubble is the same as that in ideal hydrodynamic flow round a sphere, 

 shows that the velocity of rise, u. should be related to the radius of curvature, R, in the region of 

 the vertex, by the equ-;tion u = 2/3 /gR; tht agreement between this relationship and the experimental 

 results is excellent. 



For gecaetrical ly similar bubbles of such ?. diameter that the drag co-efficient should De 

 independent -f Reynolds number, it would De expected th^t u would be proportional to the sixth root of 

 the volume, V; measurements, rf ab^ut ninety bubbles shew considerable scatter in the values of u/V 

 although there is nj systematic variation in the value cf this ratio with the volume. If u is expressed 

 in en. /sec. and V in c.cs., the exptrinents give the fcirmula U = 2U.8 V . |f this formula is applied 

 t ■ the volume :f gas given off ty the explosion of 3C0 lbs. of Amatol, the calculated rate cf rise is 

 about 17 ft. /sec. Although no direct measurements cf this vel.city have been made, this estimate Is 

 n: t inconsistont with measurements of the tin\3 between the appearance ^-f the dome and the plunie when 

 depth charges 're explojed at great depths. 



[ntruduc tion mil Experimental Method . 



The rise of gas nubbles in liquids has been studied b^ several workers', but in all the work 

 so far published, the bubbles have been so small that the results are not applicable to the study of the 

 rise of large volumes of gas, such as those produced in submarine explosions. In the experiments here 

 described, bubbles ranging in volume from i.5 to 3U c.cs. were formed in nitrobenzene contained in a 

 tank, 2 feet x 2 feet x 2 feet 6 inches filled to a depth of about 2 feet with the liquid. The bubbles 

 were photographed by spark photography at intervals of about lO milliseconds, using a revolving drum 

 camera in the manner previously described «. in some further experiments, bubbles covering ?. range of 

 volume from u.5 to 200 c.cs. were formed in a cylindrical tank, 2 feet 6 inches diameter, filled with 

 water to a depth of 3 feet 6 inches, and their mean velocity of rise over 3 mr.-asured distance was 

 determined. in both sets of experiments, the air volume <tas determined by collecting the bubble in a 

 graduated glass cylinder. 



Considerable difficulty was found in producing single, large bubbles of gas, and the method 

 finally adopted was to pivot an Inverted beaker containing air, which was then tilted so that the 

 air was released. in general, the air is released from the beaker in a stream of bubbles of varying 

 sizes, but by adjusting the rate of tilting, it was found possible to arrange that the air was spilled 

 i nto ? si nglo bubble. 



Two succrssiv; photojripns of 3 typical bubble formed in this way in nitrobenzene are shown 

 in figure 1, the time-interval between tho two photographs being 10.3 millisecs. |n addition to the 



Allen, h.S., Phil. Mag., vol. SO pp.323 iind 519 (1900). Hoefer, k, V.O.I., Vol.57, p.u7it (1913) 

 Miy^gl, 0, Tohoku Imperial university. Technological Reports, vol. 5, p.l35 (1925); Vol. 8, p. 587 (l929) 

 Phil. Mag., vol. 50, p. 112, (1925). 



« Taylor, G.I. and Davies, R.M. "Tho Motion end shape of th.' hollow produced Oy an explosion in 

 a I iquid-. 



