13 



UNDERWATER EXPLOSIONS. 

 TIME INTERVAL BETWEEN SUCCESSIVE EXPLOSIONS 



V. F. Willis 



February 194 1 



Introduction . 



It has frequently been otjservefl that an underwater explosion is followed after a short time 

 by a second explosion. The time interval may be of the order of a few seconds for large depth 

 charges, wner-ras for small detonators it is about 20 milliseconds. It is the purpose of this note 

 to submit ^n expldrv=ition of this phenomenon, to calculate the ntegnitudes of the effects to be 

 expected, ana to compare these with "ivail;-.ble experimental data. 



Description of main exper {'rental result s. 



Little information appears to be available concerning large explosions, but a fair amount of 

 work has been done in connection with small detonators. In these experiments, detonators have been 

 fired at some distance from a 2i" flat-response quartz receiver, and the resulting voltage ampl If ied 

 and spread out on a C.R.O. 



Figure 1 shows a typical C.R.O. photograph. Figure 2 shows the same thing using greater 

 amplification. Both photographs show evidence of a number of explosions which become progressively 

 weaker. The time interval between them is not constant but diminishes slowly with each uxplosion. 

 The first explosion differs from the rest in th?t it shows an instantaneous rise in pressure up to 

 its peak value. In all subsequent explosions the pressure increase is more gradual and for the 

 later explosions the pulses have a nearly symmetrical appearance. Between each pair of pulses 

 there is evidence of a small rarefaction which txtenOs over the m,=.jor part of th€ interval. This 

 is particularly noticeable in tne case of the later explosions shown in Figure 2. 



Assumptions made in cal culations . 



In the following calculations a natural explanation of all these characteristics results 

 from a consideration of what happens to the gaseous products of an explosion as they expand outwards 

 from the instant of the explosion. The fol'owing assumptions are made :- 



(i) that the explosion takes pljce in an infinitely short time. Actially, for the type of 

 detonator studied, the time interval is of the order of 2 microseconds. Subsequent 

 consideration shows that there is little change in the size of the bubble in this time 

 interval, so that little error is involv>;d in treating the explosion as instantaneous. 



(ii) that the gaseous products do not dissolve in the water to 5ny appreciable extent during 

 the short period concerned. 



(iii) that the gaseous products at all times assume the form of a spherical buoble, and behave 

 as a permanent gas. 



(iv) tnat, to a first approximation, the water ccn be treated as an incompressiole fluid. 

 The extent to which this is justified is later considered in the light of the results 

 obtained. The assumption implies t.\at there is no loss of energy Dy acoustic radiation. 



(v) that there is no dissipation of energy by thermal conduction across the face of the bubble. 



Suggested explanation of phenomenon . 



With these assumptions it is now possible to see in a general way what happens after the 

 explosion. At the instant of explosion a certain amount of gas is instantaneously generated at 



