NSWC/WOL TR 76-155 



for the fact that such dissipation must occur. In this study we 

 did so by withdrawing a fraction 3 of the energy of the oscillatory 

 motion at each extremum. 



The total energy at an extremum can be calculated from 

 Equation Al by dropping the first term and substituting from (A2) 

 and (B5) to get 



n 



H n y-1 \ V. 



-Y 



* V Mm*n 



(B15) 



4 3 



where (V M ) is the bubble volume, *n (A.. ) 



Rewriting (B5) as 



p(V) = p i (V/V ± ) 



-Y 



(B16) 



and noting that p = p(v )= P- (V„/V. ) ' and substituting 



n n c i n' i 



into (B15) we get 



Y = -JL- P n V 



n y-1 n n 



(B17) 



for the energy of the non-oscillating equilibrium bubble. 



Subtracting y from y we get the bubble energy of 

 oscillation , 



Y n Y n Y n 



(B18) 



B-9 



