178 
IV. EFFECTS OF PRESSURE WAVES 18 
1. GENERAL PRINCIPLES 
Violent effects may be produced on a small quantity of target material near the 
charge, but after the momentum given to this material has been distributed over a 
much larger mass, the velocities generated may be moderate. 
These principles are well illustrated in the familiar example of a small 
charge detonated under a few feet of water in a tank. The explosion ruptures the 
tank, for which a static pressure of 4000 pounds per square inch would be required; 
yet the water is projected no higher than it would be if issuing ffom a water main 
at a pressure of 50 pounds per square inch. The pressure that acts on the tank may 
be close to 50,000 pounds per square inch, lasting a ten-thousandth of a second. 
Against such a pressure, a tensile strength of 4000 pounds is hardly distinguishable 
from no strength at all. On the water, however, the same general effect can be pro- 
duced by the weak pressure in the main because the time of action is much longer, of 
the order of 0.1 second. 
Viewed from another angle, the water illustrates the contrast between large- 
scale and local effects. The layer of water next to the charge experiences a momen- 
tary force of nearly a million pounds per square inch and is given a velocity of 
something like 10,000 feet per second. After 0.01 second, however, the pressure wave 
will have completed several trips back and forth through the entire mass of water, be- 
ing reflected repeatedly at its boundaries, and as a consequence the momentum will 
have become distributed over the whole mass, with a very great reduction in the ve- 
locity of the water. 
The problem of determining precisely the effects of a pressure wave upon a 
target is comparatively simple only in cases of extreme simplicity. Several such 
cases will be discussed in detail in order to throw light upon the general problem. 
IV. EFFECTS OF PRESSURE WAVES 
2. SMALL TARGETS 
2. TARGET SMALL RELATIVE TO THE SCALE OF THE WAVE 
Suppose, first, that over any distance equal to the largest linear dimen- 
sion of the target, conditions in the pressure wave are nearly uniform. Then, to a 
first approximation, the flow of the water near the target can be treated as non- 
compressive, and the pressure can be treated as if it were static. 
This is easily understood on the principle, applicable to all cases, that 
the flow of the water is accommodated to the presence of an obstacle by means of im- 
pulses propagated through it with the speed of sound. These impulses serve to modify 
in the proper manner the distribution of pressure and of particle velocity. If con- 
ditions in the wave undergo little variation over a distance equal to the greatest 
diameter of the target, the impulses have ample time to keep the flow around the tar- 
get adjusted from moment to moment to the slowly varying conditions imposed by the 
oncoming wave. ~ 
