(4.40) 



THEORY OF THE SHOCK WAVE 

 Ef = f puA (e + 41^2 _|_ P\ dt 



11^5 



where A indicates the increment over the value in the undisturbed 

 fluid. 



This expression for energy flux density is convenient in calculations 

 based on the Kirkwood-Bethe theory, because the bracketed quantity 

 in Eq. (4.40) is the kinetic enthalpy increment of the fluid, which is used 

 as a fundamental variable in that propagation theory. The differences 

 between Eq. (4.40) and the expression fPudt is insignificant except for 

 very large pressures (see section 7.2). 



C. Ener-gy dissipation in shock waves. The dissipation of energy in 

 outward propagation of a shock wave as a result of pressure and velocity 



Computed from the integral ^^' /^'''^ P^ dt 

 Computed from the integral ^^ ^ ^"''^ ^ S^o ^ ^^' ^^ 



Table 4.2, Energy dissipation in the spherical shock wave from TNT. 



gradients at the shock front is greatest near the charge where these 

 gradients are largest. Experimental estimates in this region are diffi- 

 cult because of the damaging effects on measuring equipment, and at 

 the present time theoretical calculations give the best estimate of the 

 total energy radiated and the rapidity with which it is dissipated. Per- 

 haps the best estimates of this kind are afforded by the propagation 

 theory of Kirkwood and Brinkley discussed in section 4.5, in which the 

 energy plays a central role. This theory has been applied to TNT 

 using experimentally determined values of peak pressure for distances 

 greater than ten charge radii to determine the initial conditions. The 

 computed energies remaining in the shock wave at various distances are 

 hsted in Table 4.2. For comparison, values of energy flux computed 



