NSWC/WOL TR 76-155 



(3) A step decrease in the ambient pressure always results 

 in an extension of the bubble/bladder. If such a drop follows a 

 positive step where cut-off occurs at maximum bubble volume, the 

 extension beyond initial at-rest volume 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 underpressure following cut-off. 

 The effects are additive in the non-linear manner described in this 

 appendix. 



(Footnote from preceding page) 



*For a simple step pressure pulse of level p , the energy of the residual bubble 

 oscillation is given by 



Y' 2 = X 2 -Y. = ( Pl - p.) x (V. - 7 Ci ) 



where V is the bubble volume at the instant of cut-off. Thus, the energy of the 



C l 



residual oscillation and, consequently, extension of the bubble/bladder beyond 



initial at-rest volume take on greatest values for V = V and tend to zero as 



c m 



V approaches V . 

 c rr M 



A-23/24 



