378 
790 RICHARDSON, 
TABLE VI. Properties of sea water at a shock front. 
{Initial temperature 40°C; salinity 0.7 m NaCl.) 
p u U c o w X1078 h v 
(kilo-  (m/ (m/ (m/ (m/ (m/ (joule/ (cm3/ 
bar) sec) sec) sec) sec) sec)? gm) gm) 
0 0 = = 0 0 0.9993 
5 249.5 2005 2255 247.0 0.4630 5.59 -8749 
10 423.5 2360 2775 415.0 0.8870 22.75 -8198 
51 566.5 2645 3195 550.0 1.290 48.30 -7859 
20 689.0 2900 3550 666.5 1.685 78.70 7621 
25 798.5 3130 ©3865 770.5 2.065 113.5 7441 
30 899.0 3335 4150 866.0 2.445 151.0 7298 
35 992.0 3525 4415 955.5 2.815 189.5 7179 
40 1080 3705 4660 1040 3.185 230.5 .7080 
50 1240 4035 5110 1200 3.915 315.0 -6926 
60 1380 4340 5515 1345 4.640 400.5 -6813 
70 1510 4635 5900 1485 5.370 483.0 -6737 
9 
where y=(v;/v)”. With the aid of tables of n/c 
and 2; as functions of 7; and To, Eq. (2.21) may 
be solved by successive approximations giving T, 
as a function of the parameter y. Since the equa- 
tion of state, Eq. (2.12), may be expressed 
simply as p=B(7T1—273.16)[y—1], the tem- 
perature 7, may be determined as a function of 
the pressure p by a tabular elimination of y. By 
graphical interpolation, 7, is finally determined 
for the desired integral values of p (in kilobars), 
and the functions u, U, c, o, and w are then com- 
puted as functions of p by means of Eqs. (2.15)— 
(2.19). 
III. NUMERICAL RESULTS OF ARONS AND 
HALVERSON 
In fundamental shock wave studies, it is fre- 
quently necessary to know values of U—co/co 
and « at given pressure levels to the highest 
possible degree of accuracy. With this object in 
view, the calculation methods described in 
Section 2A were applied to the best available 
equation-to-state data. The numerical results are 
given in Tables I and II. A critical discussion of 
the equation-of-state data will be found in Ap- 
pendix I together with references to the sources 
from which they were obtained. 
Table I gives results for the ‘‘low pressure” 
region, covering shock wave peak pressures of 
from 0 to 1.50 kilobars (ca. 22,000 p.s.i.). The 
calculations in this table were based upon the 
Ekman equation-of-state for sea water (see Ap- 
pendix I) which is used in the calculation of 
sound velocity for echo-ranging tables. 
Since the Ekman equation deviates appreci- 
ably from experimental compressibility data at 
pressures exceeding 2 kilobars, this equation was 
abandoned in the ‘intermediate pressure’ region. 
ARONS, 
AND HALVERSON 
The results in Table II are applicable principally 
to the region between 1.5 and 14 kilobars (ca. 
200,000 p.s.1.) and are based on a careful fit of 
the Tait equation to Adams’s experimental com- 
pressibility data (see Appendix I). 
Tables I and II were computed for certain 
specific values of temperature and sea water 
salinity (equivalent to 0.675 molal NaCl), and 
it is shown in Table III that the value of 
U—co/co is not very sensitive to changes in these 
variables. 
IV. NUMERICAL RESULTS OF KIRKWOOD 
AND RICHARDSON 
In Tables IV to VI, the particle velocity u, the 
shock front velocity U, the sound velocity c, the 
Riemann o-function, the undissipated enthalpy 
w, the dissipated enthalpy h, and the specific 
volume v of sea water (0.7 molal NaCl solution) 
are presented as functions of pressure p along 
three Hugoniot curves, starting at zero pressure 
and the temperatures 0°C, 20°C and 40°C, 
respectively. These results have been calculated 
by the procedures of Part b of Section 2 and 
the data of Appendix II. The results above 30 
kilobars represent extrapolations beyond the 
range of experimental data; consequently the 
validity of the results above, say, 50 kilobars, is 
questionable. 
In closing this discussion of the calculations, 
the authors wish to acknowledge their gratitude 
and appreciation to Professor J. G. Kirkwood of 
Cornell University for his contributions in 
initiating the work and in supplying valuable 
guidance and advice. 
APPENDIX Itt 
1. Salinity and Temperature Conditions 
All calculations were made for sea water 
having a salinity of 32 parts per thousand (the 
average salinity of sea water at Woods Hole, 
Massachusetts). Salinity is defined in terms of 
directly measured chlorinity as: 
s=0.030+ 1.8050 Cl 
where s and Cl are expressed in parts per 
thousand. 
It was calculated from the average composition 
tf Equation-of-state data used in computation of 
Tables I and IT. 
