228 - 2 - 



whose diameter is comparable with 33 feet. But not when a detonator cap produces a bubble only 10 inches 

 diameter. a small-scale explosion under water with a free surface at atmospheric pressure cannot therefore 

 represent dynamically the events accompanying ?. fuU-sc-ile explosion, but if the explosion could be made 

 under water with a free surface at reduced pressure similarity in this respect would be obtained. 

 Experiments, in which bubbles wt-re produced by sparking under water and other liquids in an evricuated vessel, 

 were therefore undertaken with a view to seeing, on a small scele, what may be expected to happen to the 

 bubble in large-scale explosions. Photographs of a series of simlljr bubbles at successive stages of their 

 development were first tqken on stationary plates, but l.^ter a revolving drum camera enabled the history of 

 a single bubble to be traced. A preliminary report on these experiments is given below. 



2. the similarity relationship s. 



with ideal fluids, free from viscosity, the conditions that two bubbles whose linear scales are in 

 the ratio l:N shall be similar, are.— 



(1) h^ = Nh^ 



where h is the depth of the large-scale charge below the surface and h is that of the snail one. 



(2) P^/p^ = NP,/P2 



Where p and P are the pressures cf the air above the surfaces in tht- two cases, and p 

 and /3 the densities of the fluids. 



(3) w^/Pj = N^w^/p^ 



where w ^nd w irc the energies which tht -xplosives give up when the products of combustion 

 expand adiabat ically to infinity. 



(a) G(a^)/vj = N''G(.:-p/P2 



where G(a) represents the .vork which would be done by the gas in expanding adiabatically from 

 radius a to inf i ni ty. 



If the liquids considered in the two experiments are viscous, their viscosi t ies /:i , /x must be 

 related by 



(5) u/o^ = H'/^ Mj/Pj 



This condition ensures that the Reynold's numbers of the Iwc bubbles shall be the same at any staje. 



in the cases where the prfsr,ure in the bubbl. fills b.low th' saturation vapour pressure (s.V.P.) at 

 the temperature of tht liquid, it is n-.cessary, in order that both liquids may boil at the same stays of thf 

 expansion, that 



(6) (s.V.P. of liquid i)/p^ = N. (S.V.P. of liquid 2)/p^ 

 g. Limitation to applicability of scale relationships . 



it is imlikely that it would ever be possible to satisfy all the six above relationships simultane- 

 ously, some of them, however, are of little importance compared with others. 



After fixing arbitrarily a value for n, (1) can be satisfied by setting the charge at the correct 

 depth and (2) by exhausting the air in the chamber wht re the modfil experiment is to be carried out; (3) can 

 can be satisfied by varying the energy of tht n,xplosive charge or the sp^rk which produces the bubble. 



