1065 
DECAY OF SHOCK WAVES IN WATER. 
A. j. Harris 
Road Research Laboratory, 
London 
December 1943 
* * * * * * 
Summary. 
In 0.5.8.0. 588, on certain assumotions, Kirkwood anJ Bethe have given a comolete 
solution for the shock wave propagated into water from an explosive charge. There is, however, 
a manner in which the self consistency of the solution can be checked. Assuming that the 
pressure at the shock front decays with distance from the origin as in Kirkwood and Bethe's 
solution it is possible, thfough relations given in R.R.L. Note No. 10/17/AJH, to calculate 
the pressure gradient just behind the shock front, and to comoare it with the gradient given 
in Kirkwood and Bethe’s own solution. It is found that untii the wave has moved outwards 
five or six charge radii these values of the gradient differ by about 30 per cent indicating 
some discrepancy between form of wave and rate of decay in the carly stayes. 
A further application of the theory outlined in 10/17 inaicates that the effect of 
wave shaoe on the rate of decay Is much smaller than that due to the increasing distance from 
the orlgin, indeed if the effect of wave shace Is entirely neglected the ceak pressure at 
12 charge radi! from the orlgin Is raised only by some 20 oer cent. 
The relation between the rate of agecay of pressure at the shock front and the pressure 
gradient behind the shock front in a sohcrical wave has been given in R.R-L. Note Now 1D/17/AJH. 
If the rate of decay is known the gradient can be calculated or vice versa. It was pointed out 
by W.G. Penney that this vossibility provides a test of the self consistency cf any theoretical 
wave solution which gives both the rate of decay and tne gradient. Such a solution is that 
of Kirkwood and Bethe in 0.S.R.D. 588, for a wave in water. The test of consistency used in 
this note is a comoarison of the oressure gradient yiven in 0.S.R.D. 588 with that evaluated 
from the rate of aecay of pressure given in the same pacer. 
The solution for the shock wave in water given by Kirkwood ano aetne (O) may be written 
Xo = 
Q (R,t) = —2 Q, e @ 
R 
(1) 
eS Ne 
where 91 = kinetic enthaloy = enthaloy increment + 5 u2 
u = particle velocity 
) 
W = enthaloy increment = £ +2 - & - 9 
° 
Pp Po 
—E = internal energy 
0, P = pressure and density 
+ 
a 
time measured from instant of arrival of the shock wave at the point. 
X and y are parameters which can be calculated as functions of 4 pes being the initial 
Charge radius and R the distance from the centre of the charge: o 
Although esse. 
