458 
R 0 
Wo . 2 bAv 2 
a= Py WA pated] dre + s+ f rup a Ean) Nene) 
a, t(R) 
where the dissipated enthalpy h = E+ pAlyy is the specific enthalpy 
increment of an element of fluid, traversed by a shock wave of peak pressure 
Pen » after return to pressure Pe on its new adiabatic. Assuming the time 
integral to vanish at Ff = 00 » we have 
oe 
W, a Ld p, AV 
pA zi [eo (r)]dr + Foo , (8.13) 
4 ir rea I a a 
a) 
Subtracting Eq. 8.13 from Bq. 8.12 and transposing, we obtain 
eo 
DIR) = reupadl , 
t() 
(8.14) 
D(R) ro hp, lars + 
R 
To exclude contributions of second shocks arising from possible oscillations 
of the gas sphere, we may within the limits of approximation of incompressive 
hydrodynamic theory apply Eqs. 8.13 and 8.14 up to the time the gas sphere 
reaches maximum radius instead of to infinity. AV then represents the 
volume increment of the gas sphere to maximum radius, and pPoAVv the part 
of the energy of explosion available for secondary pulses, which may eventu- 
ally develop into shocks. 
69 
