- 3 - 15 



The total energy of the system is therefore 



V + K = 2 77'pr'r^ + (p - /') 4 77- r^ jr = A (a constant). 



The value of A is determined from the fact that at the commencement of the motion when r = r , 

 r = so that 



(p -P) U77 r^ ar 



and using this Vdlue, the energy equation Oecomes 



^^ ■■' = ^ I [ P-P] r^dr (3) 



This ejuition c^ih oe intejrited when the nature of the dependence of p on r is known. 

 It is assumed that ?.n adiaDatic law is obeyed: this of course is implied by our previous 

 assumption th':it no h-:-3t is conducted :icross th^' surf^.ce of tne DubDle. 



The 'diaDatic liw, pv' = const., jives 



37 



(«) 



Using this reljition, equation (3) becomes 



P 

 This integrates directly and gives 



II J. 



2 P„ 



■/3 (7- Dp ^■^ / (l.a) x-ax^-x-^^* * '5' 



^ /(l*a) x-ax''-x- 3r* « 



(6) 



This equation gives the relationship between r ana t and specifies the raJial motion of the bubble 

 subsequent to the explosion. The pr -ssure inside the bubble at any instant is furnished by 

 equation (6) in conjunction with (u) . 



Pressure variations inside the bubbl e . 



In order to simplify further calculations, a definite value is now given toy. For the 

 type of detonators studied experimentally a value y = 1.3 is quoted dy the makers. The value 

 •y = 4/3 is particularly convenient matherrat ically, and is near enough to 1.3, and has therefore 

 been taken. 



Equation 



