Rankine-Hugoniot Relationships

The Rankine-Hugoniot relationship expressed by Eq. (3.10) or Eq. (3.9) is shown in Eig. 3.2 as a function of 1/p andp, and such a plot is called the Hugoniot curve. The Hugoniot curve for q = 0,i.e, no chemical reaction, passes through the initial point... 

Though the form of the Rankine-Hugoniot equation, Eqs. (1.42)-(1.44), is obtained when a stationary shock wave is created in a moving coordinate system, the same relationship is obtained for a moving shock wave in a stationary coordinate system. In a stationary coordinate system, the velocity of the moving shock wave is Ml and the particle velocity is given by u = u M2. The ratios of temperature, pressure, and density are the same for both moving and stationary coordinates. 

For a transmitted shock wave advancing into any gas at an initial pressure pe of 1 atm, the RH (Rankine-Hugoniot) equation defines a functional relationship between pressure p and particle velocity w behind the wave S3, involving initial pressure, initial specific volume v, and equations of state of the target medium. Similarly, the conditions behind the reflected wave S2 and close to the product-target interface are expressible by means either of the shock wave equations or the Rie-mann adiabatic wave equations in terms of any one such variable and the conditions... 

Up, to the pressure p and specific volume v of the compressed material. The relationships are given by the Rankine-Hugoniot Equations ... 

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... 

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