Rankine-Hugoniot equations derivation

The basic equations for describing the detonahon characteristics of condensed materials are fundamentally the same as those for gaseous materials described in Sections 3.2 and 3.3. The Rankine-Hugoniot equations used to determine the detonation velocities and pressures of gaseous materials are also used to determine these parameters for explosives. Referring to Sechon 3.2.3, the derivative of the Hugoniot curve is equal to the derivative of the isentropic curve at point J. Then, Eq. (3.13) be-... 

Accdg to Dunkle s Lecture delivered at Picatinny Arsenal on Dec.13, 1955, Hydro-dynamic Theory of Detonation , (Ref 78), utilizes the laws of conservation of mass, energy and momentum to derive certain relationship known as the "Rankine-Hugoniot Equation . There are five basic equations, of which. the first three are related to five variables pressure, specific volume, energy, detonation velocity and particle velocity... 

Attenuation of shock waves in air as a function of distance was detd by R.G.Stoner W.Bleakney, JApplPhys 19, 670-8(1948) CA 42, 8475(1948). They measured the velocity of propagation produced on expin in air of chges TNT or 50/50 Pentolite 1.45 to 8 lb (either spherical or cylindrical in shape) and then caled peak pressures by applying the velocity-pressure relation derived from the Rankine-Hugoniot equations... 

The Rankine-Hugoniot relations are the equations relating the properties on the upstream and downstream sides of these combustion waves. In this chapter, general Rankine-Hugoniot equations are derived and discussed first then the Hugoniot curve for a simplified system is studied in detail in order to delineate explicitly the various burning regimes. 

The term energy per unit area is referred to as the energy fluence (Ref 8). Recalling the Rankin-Hugoniot jump conditions, specifically the mass and momentum equations for a shock, we had derived that... 

---