NSWC/WOL TR 76-155 



APPENDIX A 



RESPONSE OF GAS BLADDER TO UNDERWATER EXPLOSION PRESSURES: 



SQUARE STEP APPROXIMATION 6 



ABSTRACT 



This appendix presents the theory of the radial motion of 

 a gas-filled spherical bubble responding to step changes in the water 

 pressure. 



The theory is used to estimate the motion of a fish-bladder 

 sized bubble subjected to the pressure signature from an underwater 

 explosion. Some important qualitative results as well as some crude 

 quantitative results are readily obtained. For example: 



(1) For a simple positive step which returns to ambient 

 pressure, the maximum bladder extension depends on both the 

 magnitude and duration of the pressure pulse. If cut-off occurs 

 when the bladder (undamped oscillation) is at maximum size, no 

 extension beyond its initial at-rest size occurs . If cut-off occurs 

 at any other time, some over-extension of the bladder occurs. 



(2) A sudden decrease in the ambient pressure will always 

 result in some over-extension of the bladder. If this neqative 

 pressure (below ambient) follows a positive step with cut-off 

 occurring at maximum size, the over-extension is due solely to the 

 negative portion of the pressure signature; if not, the over-extension 

 is due to both the positive step and the negative pressure following 

 cut-off. The effects are additive in a non-linear manner described 



in this appendix. 



6. Appendix A was formerly given internal distribution as NOLTN 10205 , Goertner , 

 1974, "Response of Air Bubbles to Underwater Explosion Pressures: Square Step 

 Approximation with Application to Fish-bladder -cavity Response". 



A-l 



