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be assumed, the pressure and velocity distributions produced 

 by different amounts of the same explosive are identical if 

 referred to units of distance and time which are proportional 

 to the linear dimensions of the charges. Mathematically ex- 

 pressed, if a mass q^ of a given explosive produces the pressure 

 and velocity distributions 



45 



p = 77~(r,t) , V =T(r,t) 



(t to be measured from the start of the explosion), then a 

 mass q2 of the same substance produces the distributions 



IT 



. 1/3 1/3 



?(^) . t (J.) 



(''2) ('^2) 



Jq,)^/3 (q )l/3 



(^2) 



(1) 



Strictly speaking, it must also be specified that the initial 

 shape of the explosive be the same in the two cases, and that the 

 behavior of surrounding obstacles or surfaces, if any are present, 

 can also be scaled. This rule has long been known and applied to 

 characteristics of shock waves; it is equally applicable to bubble 

 pulsations, provided (i) and (ii) hold. 



Another homology rule which is approximately valid for 

 bubble pulsations results from the fact, which will be demonstrated 

 in the next section, that over most of the cycle the motion ap- 

 proximates fairly closely to the motion which would be executed 

 in an incompressible fluid by a bubble with no gas inside it at all. 



