10. As a further effect, the gas bubble rises and in practice the gases 
will eventually break surface. Depending on the size of charge and its 
depth below the surface, this venting may occur either before or after the 
original bubble has disintegrated into smaller bubbles with a resulting 
variation in the surface effects. 
11. The primary phenomena associated with an underwater explosion after 
detonation can, therefore, be summarized thus. First, the propagation of 
@ pressure pulse to a great distance. Secondly, oscillations of the gas 
bubble with the associated production of additional pulses each intrinsically 
feebler than the preceding one. Thirdly, the rise of the bubble under the 
indirect influence of gravity. These phenomena will now be considered in 
detail together with the modifications and additional phenomena introduced 
by the presence of the sea surface and the sea-bed. 
The pressure pulse 
Variation of pressure with time and distance 
12. For most purposes, the pressure pulse behaves simply as an intense 
sound pulse beyond a relatively small distance from the explosion. 
Therefore, the standard theory for the propagation of sound waves will be 
applicable to a study of the behaviour of the pressure pulse. Those 
points which are specially relevant to an understanding of the pressure 
pulse are treated in detail at Appendix A where it is shown that at a point 
distant r from the charge centre:- 
pete et - 3) eee 
where 
t = time interval after the initiation of the explosive charge 
f = mass density of water 
c = velocity of sound in water 
P = pressure in pulse (additional to the hydrostatic pressure 
existing prior to the pulse) 
Equation 4 gives the pressure p as a function of the two variables, r and t. 
Such a relationship can be represented graphically by a surface in a three 
co-ordinate system. The dependence of p upon r and t is illustrated by 
the surface of arbitary shape shown in fig. 1. 
However, it is instructive to study the variation of p with change in 
only one of the two variables, the other remaining constant. Thus the 
plane curve ABC gives the variation of pressure with time at a constant 
distance r, from the explosion. Similarly, the variation of pressure with 
distance at a constant time.t, after the explosion can be studied from the 
plane curve, FED. 
Variation of pressure with time (distance constant) 
13. To understand the physical significance of equation 1, let Pp, denote 
the pressure at time t,; and distance r, and let p, denote the pressure at 
time t, and greater distance r,. Then from equation 1 
p, =!/r, 2(t, - 3) bie | ecatNSstie Side: | peeo> ene (2) 
