MOTION OF THE GAS SPHERE 329 



The internal energy term E{a^)/Y depends on the hydrostatic pres- 

 sure at the depth of explosion. If the equation of state per gram of 

 explosive is taken to be of the form PV^ = k in cgs. units, the internal 

 energy E{a) in ergs for W pounds of explosive is 



E(a) = 454TF PdV = 454Tf 



/, 



7 — 1 7—1 



Expressing this in terms of the radius a in feet by the relation 



454Tf 7 = — (30.5a)3 gives 

 o 



E{a) = ^^ (3.81 X 10-3)7-' "^"^ 



7 - 1 ' ' a3(T-i) 



The available energy Y in ergs for W pounds of explosive can be 

 written as a fraction r of the detonation energy Q in calories per gram 

 of explosive as 



Y = (4.19 X 10^) rQ (454Tf) 



and the desired fraction is therefore 



E{a) ^ (3.81 X 10-3)7-1 k ^7-ia-3(7-i) 

 Y " 4.19 X 10^ '7-1 rQ 



To express this in terms of the nondimensional radius a*, it is necessary 

 to evaluate the scale factor L* in feet, which is 



(8.54) L*(ft.) 



/ 3F y 



\4:irpo(jz„/ 



(5.17^)" 



if Zo is in feet. The time scale factor C* is not needed here, but is given 

 for completeness; its value is 



*^ -1/2 



^-) = 0.216 L 



2gzo/ 



where C* is in seconds, L* and Zo in feet. Using the scale factor gives 

 for the internal energy term 



