1067 
-3- 
where v = soecific volume of fluid just behing front 
velocity of souns in fluia just behine front. 
. a 
(9) gives us anotner expression for ——— 
3 () 
00 = i ES +4 (10) 
a 
Pt ttl) % 
The coefficients A and 8 have been comouted from the data of 0.S.R.D, 676 and are given in 
Table 1, The two values of 2£_ as derived from (6) and (9) are shown in Figure 1 where 
3 (2) 
it is seen that until the wave has crogresseo some five charge radii there is a discrecancy of 
about 30 per cent vetween the two values. At distances less than seven charge radii the value 
from (10) is less than that from (6), beyona this distance tne relation is reversed. 
o 
u 
Oo 
It may be worth while ccinting cut nere that close to the charye tne term aS in (9) 
OR 
Is not of much imoortance in comparison with 8 + Since B is a known function of po the equation 
° 
is now integrable In the form 
go. 
B 
; a 
or oc - log =a (11) 
8 R 
eh 
where 9) is the oressure in the wave at tne moment of initiation. 
In Figure 2 is shown the value of 98 as a function of = derived from (11) together 
° 
with the value derives from the theory of 9,S,R.0. 588, {t is secn that at first the effect 
of shape is to delay the attenuation, then at about 2.5 ap from tne centre to increase it. 
The effect of shape is not very large, for examcle at 12 ag from the centre where the pressure 
has fallzn to about 1/30 of the initial value the aifference between the curves is some 22 ver 
cent. This shows that tne rate of decay near to an exolosive of this tyoe is not likely to 
deoend much on anything but the initial oeak value of the oressure. 
TABLE 1. 
° A 8 ) A B 
KILOBARS | NON-DIMENSICNAL KI LOBARS KPLOBARS NON-DIMENSIONAL KI LOBARS 
References. 
(a) The Decay of Plane, Cylindrical and Soherical Shock waves 10/17/AJH. 
(b) Progress Reoort on "The °ressure Wave >roducea by an Underwater Exolosion |*, 
J.G. Kirkwood and H.A. Bethe. 0.5.R,D. 588. 
(c) Progress Reoort cn "The Fressure Wave Produced by an Underwater Explosion ti*, 
J.G. Kirkwood and E,W. Montroll.,  0.S.R.D. 676. 
