NSWC/WOL TR 76-15 5 



Equation A19 gives the equilibrium radius A (radius after the 

 oscillation has damped out) for the bubble in the n state. 

 A19 is derived from (A18) by setting P (A) equal to p 



n 



10. Bubble Motion in State 1. Consider the step change 

 in outside pressure from p, to p.. In accordance with the jump 

 conditions (A8) and (A9) and the initial conditions (All) and (A12) 

 we set A = and A = A. in (A7) to obtain the total energy 



Y l = ( Pl + Y=T> V i 



(A21) 



where we have also used Equation A2 to evaluate the internal energy 



E(A.) 



11. Since A = 0, the oscillation in state 1 starts at an 



extremum. Whether this extremum is a maximum volume V„ or minimum 



M 



V" m is determined by p being "greater than" or "less than" p.. 

 If p, > p . , then 



A M X = A i (A22) 



P Mi = Pi (A23) 



IF p. < p. , then 



\ = A i < A24 > 



P n - Pi (A25) 



A- 8 



