23 
#09 66. Underwater photography and 
piezu-electric gauges have been 
used to obtain considerable 
empirical data on bubble motion 
resulting from small explosions 
in experimental tanks. 
Qualitatively, experiment 
100 confirms the theoretical 
predictions that the bubble will 
oscillete while rising and that 
it will send out a4 pulse at each 
minimum, the pressures in each 
pulse being small compared with 
those in the original pressure 
pulse but of longer effective 
0:26 0:27 028 029 o:3 duration. Quantitatively, the 
TIME~ sac. theory has given good predictions 
of observed period of first 
oscillation and the rise during 
Fige11 - Calculated pressure/time this period. The theory cannot, 
PRESSURE — Ib per sq in 
variation of first bubble however, predict with much 
pulse accurecy the form and magnitude 
of the first bubble pulse and the 
curve shown in fige11 should not be regarded as an accurate quantitative 
prediction. This defeot of the theory was expected since the collapsing 
bubble tends to become unstable and depart from spherical shape and may even 
split into separate smaller bubbles which coalesce into a single bubble 
again on re-expansion. Further, near the minimum radius where changes are 
rapid it is no longer a good approximation to neglect the effects of 
compressibility. In general, therefore, the theory cannot be expected to 
predict with accuracy any quantity depending primarily on events when the 
bubble is near its minimum radius. It may be noted that although in fig.10 
the most pronounced rise occurs near the minimum radius, this rise depends 
mainly on upward momentum acquired when the bubble is large. (The force 
producing the momentum is the buoyancy of the bubble which increases with 
the size of the bubble). The breakdown of the theory when the bubble is 
small does not, therefore, invalidate its use for estimating the rise of 
the bubble in the first oscillation. 
67. With suitable sizes of charge and depths of explosion, several 
oscillations of the bubble may take place before it breaks surface or 
degenerates into smaller bubbles. The period of the second and later 
oscillations and the associated rise owing to the net hydrostatic force 
cannot, in general, be predicted with the same accuracy as the initial 
oscillation and rise. This further defect of the theory is undoubtedly 
associated with loss of energy during oscillation due to such causes as 
turbulence which are not allowed for in the theory. Due to this loss of 
energy, the later oscillations tend to become more rapid. For example, 
in an experiment with 1 oz. charge of Polar Ammon Gelignite exploded at a 
depth of 7 ft. in 15 ft. of water the periods of the first, second and 
third oscillations were found to be 0.072, 0.049 and 0.035 sec. 
respectively. The associated energies of the bubble motion would then be 
about 9000, 3000 and 1000 calories for the successive oscillations 
indicating that for this case about two-thirds of the energy was 
dissipated in each oscillation. 
