578 



Temperley^9) in Great Britain, and Herring^), Kennard^^), Shiffman and 

 Friedman^l) in the United States. In this section, the experimental results 

 described previously in this report will be compared srith the theory 

 subject to the following assiimptions: 



i. the liquid is regarded as an inviscid, incompressible medium of 

 unlimited extent, 

 ii. the vertical motion of the center of gravity of the bubble is 

 considered to be negligible, 

 ill. the kinetic energy of the gas is neglected, 

 iv, the expansion and contraction of the gas is assumed to be adiabatic 

 and to follow the equation 



pv'^ - c (9.1) 



appropriate for an ideal gas. 



Under these conditions, it is convenient to introduce non-dimensional 

 definitions of the radius and time, in accordance with Ref. (21), which 

 have the forms 



A - La (9.2) 



T = Ct (9.3) 



in vrtiich A and T are the actual radius and time respectively, a and t are 

 the non-dimensional radius and time respectively, and the length and time 

 scaling factors are defined by the following eqiiationss 



J^ '^' . 1.729 (^)^' ^ '^' (9..) 



Qo V2 Wo W^3 



^ L - O.m (rQ)^3 ^^ (9.5) 



where W is the weight of the charge, Q the detonation energy per unit weight, 

 r the fraction of the detonation energy remaining in the bubble motion after 

 passage of the shock wave, po the initial, hydrostatic pressure at the depth Zq 

 (which includes the equivadent depth of the atmosphere) where the bubble is 

 formed, and /> the density of the liquid medium; the numerical factors in the 

 third members of Eqs. (9.4) and (9.5) are appropriate for L and Zq in feet, 

 C in seconds, rQ in calories per gram, W in pounds, with ^ = 1.025 (sea 

 water). 



-22- 



