170 
III. PRESSURE WAVE 10 
3. QUALITATIVE THEORY 
When the detonation wave in the explosive reaches the surface of separation 
between explosive and water, it compresses the adjacent layer of water almost instan- 
taneously and at the same time gives to it a high velocity outward. The outward rush 
of this layer then compresses the next layer, and at the same time the high pressure 
in the first layer gives a high velocity to the next layer. Continuation of this 
process results in the propagation of a state of high pressure and large particle ve- 
locity outward as the front of a diverging spherical pressure wave in the water. As 
the wave moves outward and becomes spread out over progressively larger areas, its 
intensity decreases, ultimately in inverse ratio to the distance from the center. 
Meanwhile, the gas maintains the water next to it at a high pressure, and the state 
of pressure and of motion in this water is continually propagated outward to form 
subsequent portions of the pressure wave. 
As the gas expands, however, its pressure falls; the expansion should be 
nearly adiabatic, because of the rapidity of the expansion. The laws of ideal gases 
will not apply at first, however, because the density is then almost equal to that of 
the solid explosive. In the pressure wave, therefore, the pressure and the particle 
velocity should decrease behind the front. Thus a short time after the explosion 
occurs the distribution of pressure p and of outward particle velocity u in the water 
should be somewhat as shown in Figure 5, provided elastic oscillations within the 
gas globe itself are ignored; the abscissa r represents distance outward from the 
center of the original explosive mass, which is assumed spherical. The distance 
marked "gas" is the radius of the globe 
of gas at the instant in question; pressure 
and particle velocity within the gas are not 
shown. The distance marked "original solid" 
is the radius of the original sphere of ex- 
plosive material. 
As the gas continues to expand, 
0 Radius r its pressure will eventually sink to the 
hydrostatic pressure p, proper to the depth 
at which the explosion occurs. If we were 
Figure 5 
dealing with a one-dimensional case and hence with plane waves, the particle velocity 
u would now be zero and the expansion of the gas globe would cease. 
In the case of diverging waves, however, we have to reckon with the "after- 
flow," described in Appendix I, Section 1, topic: Spherical Waves. The passage of 
a spherical pressure wave through the water leaves the water flowing outward, with a 
velocity roughly proportional to the inverse square of the distance from the center. 
Perhaps the pressure wave itself is to be identified with the Phase 4 of some writers, 
and the afterflow with Phase B or the "surge." The term afterflow is preferred here 
because, after all, even in the pressure wave there occurs a powerful, albeit short- 
lived, forward "surge" of the water. The distribution of pressure p and of result- 
ant particle velocity u, including the velocity of afterflow, at the instant when p 
