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APPENDIX 6 PRESSURE DISTRIBUTIOW IN 



N0N-C0I.1PRESEIVE RADIAL MOTION 



The Euler equation for radial flov/ is 



dv - ^v , „ dv _ .1 djp ... 



Intecratinc this from r to infinity and writing 

 oo 



dr so that v - •= .^.T,, lo\ 



9 r * ' 



we find, ass\jrainG P constant 



P - P^ s ^ 1^^ ' ^ v'' (3) 



For non-compressive motion outside a bubble of radius a 



we have 



s. do. , . 



V = ^ ^ (4) 



so that ^ 



^ = V ^ (5) 



Substituting (4) and (5) into (3) gives 



P - P s Pa"^ £» 4„ gga /da) „ ea /da^ /gj 



Setting r«a gives 



PO) -P«= ?»§^-<-^ (^/ (7) 



and solving (7) for d a and inserting in (6) gives finally 



(8) 



