UNDERWATER EXPLOSION PHENOMENA 
computed and plotted in Figs. 8, 9, and 10. 
Figure 8 shows curves for the initial positive 
phase, i.e., up to the time at which the excess 
pressure at the point of observation becomes 
zero following the arrival of the shock wave. 
This figure is for a charge depth of 500 ft. only, 
but a similar one for a depth of 250 ft. would not 
be very different. Figures 9 and 10 show the same 
curves extended to the time of first bubble 
maximum for depths of 250 ft. and 500 ft., 
respectively. They are essentially the same in 
form, the principal differences being due to the 
longer negative phase and smaller negative pres- 
sure at the 250-ft. depth. The functions plotted 
in Figs. 8, 9, and 10 are: 
a. Irreversible energy flux, given by 
Fi= 
ery 6x10-Pal f (Ap)2dt. (32a) 
polo 
b. Afterflow : the afterflow energy flux should, 
according to the criterion of Section 5, average 
out to zero because it does not represent a 
radiated or an irreversibly stored energy. After- 
flow energy flux is given by 
1 t 2 l? 
r.-——(f apdt) =) 
2poR 0 2poR 
Since the total impulse up to ¢=¢y1 is very small, 
(32b) 
1147 
529 
the total afterflow energy up to this time is also 
very small. Physically what has happenéd is 
that the afterflow velocity was always outward, 
while the excess pressure was first positive, then 
negative. At one time the afterflow was with the 
pressure, later against it so that the total work 
done because of the motion has a net value that 
is very small, while each of its positive and 
negative components are large in magnitude. 
c. Impulse: the impulse is defined by 
t 
r= fap 
0 
d. Particle velocity: the total particle velocity 
is given by 
Ap k 
a A f Apdt. 
polo poR Yo 
(29) 
(30) 
Separate curves for each component of the 
particle velocity have not been plotted, since 
their form may be obtained directly from the 
pressure-time and impulse-time curves. The form 
of the total particle velocity curve will change 
with the distance from the charge, since the two 
components vary as the first and second powers 
of the radius, respectively. The curves shown 
apply to the specific case where R= W3/0.352. 
(PS!) 
PRESSURE 
Excess 
END OF POSITIVE PHASE, 250 FT. DEPTH 
Fic. 7. Composite pressure-time curve for entire shock wave. Explosive: ‘NT; distance from 
center of charge: K= 
W1/0.352. Legend: @ time constant of initial shock wave decay. 
initial portion of shock wave from measurements by J. S. Coles et al., Woods Hole. -— 
— tail 
of curve from Fig. 5, 250-ft. depth. - - — — tail of curve from Fig. 6, 500-ft. depth. 
