186 



vi 







Figure 2 - Calculated Time-Displacement Curves for Undamped Oscillation 

 of a Bubble or Globe of Gas under Water 



R - radius 

 R^ = radius when in equilibrium 



t — time 

 T^ = period of very small oscillations 



The time relations of pressure variation are also studied in the 

 report, and the conclusion is reached that though the peak of first compres- 

 sion is lower than the initial pressure peak, it is still high enough to give 

 rise to a wave of compression in the water. Since this first compression 

 peak is broader than the initial shock wave, it may carry with it an impulse 

 exceeding that of the high-pressure part of the primary pressure wave. 



The calculations discussed in this report deal mainly with the hy- 

 drodynamic phenomena in an incompressible fluid; however, at each pressure 

 peak the compressibility of the water enters to play a part, and energy is 

 radiated in a shock wave. Especial interest attaches to the quantity of en- 

 ergy lost in this way because it acts in structural targets in a different 

 way from that associated with the slower motion of pulsation. No valid meas- 

 urement of the energy in the shock wave is yet available, and in particular 

 its value relative to that of the energy of oscillation E is still a matter 

 of opinion. 



The analysis thus applied to the pulsations of large gas globes re- 

 sulting from explosions also explains the curious effect known to be caused 

 by the presence of small bubbles suspended in water traversed by a shock wave. 

 It is shown that these may serve as radiating sources of new shock waves 



