WATER 
by log(vL0, S]/vLp, S]), and (2) the calculation 
of quantities defined by line integrals along 
adiabatics is greatly simplified by taking S 
instead of T as one of the independent variables. 
The function A[.S] is related simply to c;, the 
sound velocity at zero pressure and entropy S 
according to Eq. (2.4) as follows 
AES —ci2/non;s  ci—cO} S|: (2.14) 
On the basis of Bridgman’s p-v—-T data for pure 
water, an average value of 7 equal to 7.15 has 
been selected for the present calculations. In 
Section 2 of Appendix II, it is shown that x 
deviates from this value by less than 4 percent 
in a large pressure-temperature field bounded by 
adiabatics starting at zero pressure and tem- 
peratures of 20°C and 60°C, respectively, and 
extending to pressures of 25,000 kg/cm’. We 
assume that has the same value for an aqueous 
0.7 molal NaCl solution as for pure water, and 
we obtain by interpolation the required values 
of B(t) from R. E. Gibson’s values of B(t) for 
dilute aqueous NaCl solutions (see Appendix II, 
Section 1). The appropriate heat capacity and 
thermal expansion data are discussed in Section 
1 of Appendix II. 
We now proceed to the calculation of the 
quantities u, U, c, ¢, and w. We first express these 
quantities with use of Eq. (2.12) in terms of p, 
v=v(p, T)=vLp, S], vo=v(0, To), 
v1=0(0, 71) =2[.0, S], and c1=c(0, 71) =c[0, S] 
(see Eqs. (2.1)—(2.6), also Fig. 1) as follows: 
u=[p(vo—2) }, (2.15) 
U=pvo/u, (2.16) 
C—G Ui) 0) te)! CDE yp) 
2c, 
c= [(a1/v) *-PP—1], (2.18) 
a 
cr 
a= [(v1/v)"—1], (2.19) 
n—1 
Once the temperature 7), to which an element 
of fluid returns along the adiabatic intersecting 
the Hugoniot curve at (p, 7), is determined, all 
of the above quantities may be determined as 
functions of p. To accomplish this, the enthalpy 
increment, AH, occurring in the third Hugoniot 
condition, Eq. (2.3), is written as the sum of two 
line integrals, the first along an isobar from 
ACh Eh aawON aD TOR VAD SHOCK: 
377 
WAVE 789 
(0, To) =[0, So] to (0,7:)=[0,S] and the 
second along an adiabatic from (0, 7:) =[0, S] 
to (p, T)=[p, S] (see Fig. 1), giving: 
AH=w-+h, 
w= f vp’, S|dp’, (2.20) 
0 
Ss Ty 
h= T{0, styus’= f Ga (Olea) die 
Tr 
So 0 
where w is the undissipated enthalpy already 
defined by Eq. (2.6) with p)>=0 and given ex- 
plicitly in terms of ci, v1, and v in Eq. (2.19). 
The dissipated enthalpy h can be determined as 
an explicit function of 7) and T; from specific 
heat data (Appendix II, Section 1). Combining the 
third Hugoniot condition, Eq. (2.3), with Eqs. 
(2.19) and (2.20) we obtain the relation 
h 1 n+1 
= |» gt | 
cy Qn n—1 
V1 —V0 
= G=)l), 12-21) 
nv, 
TaBLE IV. Properties of sea water at a shock front. 
(Initial temperature 0°C; salinity 0.7 m NaCl; Co= 1443 
m/sec.) 
Dp u U c o w X10-6 h v 
(kilo-  (m/ (m/ (m/ (m/ (m/ (joule/ (cm3/ 
bar) sec) sec) sec) sec) sec)? gm gm) 
0 0 = = 0 0 0 0.9915 
5 257.0 1930 2190 253.5 0.4565 6.740 8593 
10 433.0 2290 2720 420.5 0.8720 25.80 8040 
15 575.0 2585 3145 552.0 1.270 54.40 7710 
20 697.5 2845 3510 664.0 1.655 86.55 «7483 
25 805.5 3075 3835 763.5 2.030 122.5 .7319 
30 905.0 3285 4125 855.5 2.405 160.5 .7186 
35 997.0 3480 4395 940.5 2.770 201.5 -7075 
40 1080 3665 4640 1020 3.140 244.0 .6989 
50. 1240 5095 1175 3.860 331.0 -6842 
60 1385 4300 5495 1315 4.575 419.0 .6728 
70 1515 4585 5870 1455 5.285 509.0 6641 
80 1635 4855 6225 1585 6.000 595.5 .6579 
90 1740 5120 6570 1705 6.730 676.0 -6542 
TABLE V. Properties of sea water at a shock front. 
(Initial temperature 20°C; salinity 0.7 m NaCl; Cp=1517 
m/sec.) 
p u U c o w X10-6 h v 
(kilo- (m/ (m/ (m/ (m/ (m/ (joule/ (cm3/ 
bar) sec) sec) sec) sec) sec)? gm) gm) 
0 0 — _ 0 0 0 0.9929 
5 251.0 1975 2230 248.5 0.4595 5.570 8668 
10 425.5 2335 2755 415.5 0.8790 23.45 8120 
15 567.0 2630 3175 549.0 1.280 49.35 7787 
20 689.0 2880 3535 663.0 1.670 80.05 7555 
25 798.0 3110 3855 765.0 2.050 115.0 .7381 
30 897.5 3320 4140 859.0 2.425 152.5 7243 
35 990.0 3510 4405 946.5 2.795 192.0 7130 
40 1075 3690 4650 1030 3.160 233.0 7034 
50 1235 4020 5100 1185 3.885 317.5 6880 
60 1380 4325 5505 1330 4.605 404.5 .0705 
70 1510 4610 5880 1465 5.320 489.5 .6679 
80 1625 4885 6240 1600 6.050 573.5 -6626 
