HYDRODYNAMICAL RELATIONS 39 



where n is a constant and B a function of temperature only. Use of 

 this equation to determine {dV/dT)p and {dV/dP)T, together with 

 values of V{T, 0) and Cp{T), then enable the calculations already out- 

 lined to be made. This procedure was used for the original calculations 

 on pure water. For the calculations on salt water a somewhat different 

 scheme of calculation was set up, based on a modified form of the Tait 

 equation. It was found convenient to make calculations of shock front 

 conditions by integrations along paths of constant pressure and entropy, 

 and for this purpose the equation of state was taken to be of the form 



^^■^°^ ~v[dp)s^n[P + BiS)] 



or in integrated form 



where B{S) is a function of entropy alone and n is approximately a con- 

 stant. It was found that the necessary value of n to fit P-V-T data 

 between 20° and 60° C. up to pressures of 25 kilobars deviated by less 

 than =b 4 per cent from an average value 7.15, which was adopted for 

 the calculations. The slowly changing constant B{S) was taken to be 

 the same as the value B{T) determined for 0.7 molal salt water from 

 data of Gibson. At 20° C, B has the value 3.047 kilobars. 



This form of equation of state should give a better extrapolation of 

 the P-V-T relations to high pressures than the isothermal Tait equa- 

 tion, which permits a state of zero volume for finite pressure and hence 

 must overestimate the compressibility and related sound wave veloci- 

 ties at high pressures. With the adiabatic form of equation and values 

 of V{T, 0) and Cp from the literature (cited in Table 2.1), the enthalpy 

 CO, particle velocity u, sound and shock velocities c and U, and Riemann 

 function a can be computed by straightforward methods. Results for 

 sea water initially at 20° C. are given in Table 2.1 for pressures up to 

 80 kilobars (1 kilobar = 14,513 Ib./in.^), and plotted in Fig. 2.3. 



Although they are not directly needed, the change in entropy and 

 temperature rise at the shock front are of interest and approximate 

 values are given in Table 2.1 for several pressures. The entropy change 

 is worth consideration as Kirkwood and Bethe in their propagation 

 theory neglect its contribution to the enthalpy of the shock wave. This 

 contribution is given by 



Aco(^) = TiPo, S) dS 



^ So 



