fe (du ple (2b) -- ang | 
Ite) On OFZ OR 
(d's it ns) 280009 | 
(24) + UR) ay (sb) & aba ie a 
[in = PC Pa) , Alba Ge Fin) 
where g = Poll du Ap, =f: d Log U/d fog Pin and where the prime indicates 
(8.8) 
that the partial derivatives are to be evaluated at the shock front. The 
seuvet awed is to be calculated from the first of the Hugoniot relations, 
Eas. 8.6, All coefficients in Eqs. 8.8 can be expressed as functions of 
pressure alone by means of the Hugoniot conditions and the equations of 
state of the fluid. 
We now desire to establish a supplementary relation to permit the 
formulation of an ordinary differential equation for the peak pressure as a 
function of distance from the charge without explicit integration of the 
fundamental equations of hydrodynamics. The physical basis for the supple- 
mentary relation to be established lies in the faeh that the nonacoustical 
decay of waves of finite amplitude is closely associated with the entropy 
increment experienced by the fluid in passing through the shock front and 
the accompanying dissipation of energy. As a shock wave passes through a 
fluid, i. leaves in its path a residual internal energy increment in each 
element of fluid determined by the entropy increment produced in it by the 
passage of the shock front. As a consequence, the energy propagated ahead 
by the shock wave decreases with the distance it has traveled from the source, 
67 
