Hh 



MOTION OF THE GAS SPHERE 



infinite body of water are in the proper direction. No precise data 

 suitable for directly determining the constant in the simple period ex- 

 pression were available, and its value was therefore obtained by assum- 

 ing that 43 per cent of the computed detonation energy of 1,060 cal./gm. 

 for TNT remained in the first pulsation. 



Friedman (37) has outlined a procedure whereby the agreement of 

 the observed periods with the theory including surface effects can be 

 checked, and which also permits estimates of the energy in the bubble 

 motion if the theory applies. The theoretical expression, Eq. (8.68), 

 can be written 



T{d -f 33) 



5/6 



a- ^ 



F\x) 



d{d + 33)1/^ 



where a = OMl{rQWy'\ (3 = 0.192{rQWy'', and 

 F'{x) = - (1 + x)F{x) (see footnote 12) 



1.0 



^ 0.9 



O 

 O 



cr 



0.7 



06 



0^ 



^■''o 10 20 30 40 50 60 70 80 90 KX) 



CHARGE DEPTH (FT) 



Fig. 8.21 Bubble periods for 300 pound TNT charges fired in 100 feet of 



water. 



A plot of Ti {d + 33)5/6 against F'{x)/d{d + 33)^/^ should therefore be 

 a straight line of slope /3 and intercept a, from which {rQWy^ can be 

 evaluated. The result is shown in Fig. 8.22. For depths greater than 

 60 feet, the points depart considerably from a straight line, indicating 

 failure of the rigid bottom correction. Fitting the points at shallower 

 depths by the straight line indicated gives rQ = 424 cal./gm. from the 

 value of /3, and rQ = 490 cal./gm. from the value of a. The mean 



