HYDRODYNAMICAL RELATIONS 29 



wave pressures for a number of explosives.^ In this attack, the hydro- 

 dynamical equations are considered in a somewhat different way than 

 the one already outlined. 



Kirkwood and Bethe consider the solution of the fundamental equa- 

 tions by introduction of a new variable, the enthalpy H defined by the 

 relation 



(2.19) H = E + - 



P 



where E is the internal energy per gram of fluid. If Ho is the enthalpy 

 of the undisturbed fluid ahead of the shock wave, the change in enthalpy 

 0) = H — Ho, and we have 



doj = dE + 



'--"if) 



From the second law of thermodj^namics 

 dE = TdS - Pd- 



and it follows that 



(2.20) dco = TdS + - dP 



P 



Behind the shock front it is assumed that dS = 0, and numerical cal- 

 culations show that the change in enthalpy at the shock front from 

 dissipation are only a few per cent of the total (see section 2.6). The 

 enthalpy calculated on the basis that dS = is thus a good approxima- 

 tion, and it proves possible to obtain approximate solutions of the 

 equations of motion, expressed in terms of the enthalpy, in a form to 

 which boundary conditions at the gas sphere can practically be applied. 

 The details of this solution will be treated more fully in Chapter 3. It 

 is desirable, however, to outline the initial steps of the analysis at this 

 point, as they follow immediately from the fundamental equations, and 

 the necessary conditions for the propagation theory at the gas sphere 

 and the shock front must also be put in suitable form for their appli- 

 cation. With the assumption dS = 0, we can, from Eq. (2.20), write 



* A series of reports on various stages of these calculations have appeared in 

 NDRC Division 8 Interim Reports (113). The final results are collected and dis- 

 cussed in two OSRD reports by J. G. ffirkwood, S. R. Brinkley, Jr., and J. M. 

 Richardson (59, V and VII). Other related reports by Kirkwood et al are also 

 Hsted in Reference (59). 



