179 
19 Be EFFECTS OF PRESSURE WAVES 
2. SMALL TARGETS 
The pressure upon a small target can conveniently be resolved into two 
parts: 
(a) the pressure p that would exist at the same point if the target 
were repleced by water, and 
(b) an additional "dynamic" pressure, positive or negative, caused 
by motion of the water relative to the target. 
The magnitude of this additional pressure can scarcely exceed 
pu?,where p is the density and u is the particle velocity in 
the wave. 
Thus, a pitot tube, emall as compared with the thickness of the pressure 
wave and turned toward the side from which the wave approaches, would read the value 
of 
p +1pu? 
Again, if the target has an axis of symmetry in the direction of propagation of the 
wave (this axis constituting, therefore, a streamline), the pressure at the point on 
the front face where the axis cuts the surface of the target will be p+ pu’. 
In pressure waves in water, however, pu” is much smaller than Dean Ute as 
is usually the case, the linear or small-amplitude theory can be used for the wave, 
and if for the moment we neglect the afterflow, we have p=pcu (cis the speed of 
sound), hence . 
[OO ee as 
p ¢ 
In practical cases u is much smaller thanc. For example, at 25 feet from 300 pounds 
of TNT, u <50 feet per second, hence u/c <50/4930 = 1/100. In blast waves in air, cn 
the other hand, pu? tends to equal p. 
The afterflow velocity at the point just mentioned can be estimated from 
the third term in Equation [3] in Appendix I. The value of [pdt at that point is 
about 2 x 1.45 x 144 pound-seconds per square foot, r = 25 feet, and p= 1.94 slugs 
per cubic foot, hence the term in question gives an afterflow velocity of only 8 feet 
per second. ‘Thus even at 25 feet from 300 pounds of TNT, which is well within its 
damaging range, dynamic effects of the afterflow or "surge" will usually be small. 
One effect of the wave is a tendency to set the target in motion in the di- 
rection of propagation of the wave. The acceleration results from the combined ac- 
tion of the pressure gradient in the wave and, if there is relative motion between 
target and water, of the dynamic pressure pu? and of viscosity. Minute suspended 
objects will tend to undergo the same displacement es does the water itself. Larger 
objects, if free to move, will’be displaced less. 
If the target can be crushed, its deformation will be determined almost 
wholly by the major component of the pressure on the target, which is the pressure in 
