457 
The work w(K) done by a spherical shock wave on the fluid ex- 
terior to a sphere of radius A is 
° é 
WR) = 47 | fr( ht] u(pt po) dt, (2.9) 
t (R) 
where P and tt denote excess pressure and particle velocity behind the shock 
front, t() the time of arrival of the shock front at point Fr » and r(FA,t) 
the H#uler coordinate of a particle of initial Lagrange coordinate Rh. The 
integral is along a path of constant Lagrange coordinate R - By the second 
law of thermodynamics,we assume that after the shock wave has traveled to 
infinity, the work W(R ) » delivered to the fluid beyond H » is dissipated 
to internal energy of the fluid, each particle of fluid returning adiabati- 
cally to a state of thermodynamic equilibrium of pressure p and an entropy 
° 
exceeding its initial entropy by the increment corresponding to the peak 
pressure at which the shock front crossed it, 
The adiabatic work W, (equal to the energy of explosion) done by 
a spherical charge of explosive of initial radius a, on the exterior fluid is 
K oe 
Woe Pols, El fol ted 4 7, +] ru (f tRALE, 8,20) 
Ao C(n) 
where E is the specific energy increment of the fluid at pressure fe and for 
an entropy increment corresponding to shock-front pressure b « Now, 
1 © : 2 AV 
b. ur *At = bf Pail dr + bo 2 (¢.11) 
ab Bt 
where fis the final density of the fluid, and AY is the volume increment of 
the gas sphere composed of the explosion products. Using Ea. 8.11, we com- 
bine the last term of the time integral with the first integral to obtain 
68 
