582 



10. Determination of the Bubble Energy 



Combination of Eqs. (5.1), (9.3), and (9.5) gives an equation for 

 rQ in terms of the experimental period constant 



rQ - 19.2 (I) (10.1) 



while a similar combination of Eqs. (8.1), (9.2), and (9.4.) gives an 

 eqiaation for rQ in terms of the experimental radius constant 



rQ = 0.19it {^Y (10.2) 



Making the natursJ. asavunption that rQ is independent of the depth and 

 noting that t and ajj are slightly depth dependent through the ptirameter k. 

 It is expected that the proportionality "constazits" J and K will vary 

 directly with ay and t. If such variation of J and K with depth had been 

 measurable with sufficient precision over a wide enough range, it would 

 have been possible, in principle, to determine uniquely the paraiieters 

 T and k as well as rQ. Since, however, such variation was masked by 

 the experimental error in J and K for the small range of depths actually 

 observed*, it has not proved feasible to make a unique calciilation of 

 these parameters. Therefore the two Eqs. (10.1) and (10.2) were first 

 used to eliminate rQ with the result 



^ = 4.62 4 (10.3) 



a.. 



The observed values of the period and radius proportionality constants were 

 used to compute the apparent value of t/«^. Reference to Fig. 3 (which 

 was obtained from tile figures in Tables XX and XXI) then jlIIows the 

 determination of k for an arbitrarily chosen nr . The non-dimensional 

 period and radius then become determinate, and a value of rQ may be 

 obtained which is consistent with both the radius and period data. In 

 Table XXII, these energy values are given for the first period of 

 oscillation of severed, of the explosives described previously in this 

 report . 



* Although the depths varied by about two-fold, k depends upon depth to the 

 1/2 power or less, and a» and t are not very sensitive to k. 



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