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Rankine-Hugoniot equations

These equations can be combined to eliminate the velocities, yielding the Rankine Hugoniot equation for internal energy jump in terms of pressures and specific volumes (V s 1/p)... [Pg.11]

The Hugoniot can be described with a differential equation by taking the total differential of the Rankine-Hugoniot equation (2.4)... [Pg.16]

Since this equation came directly from differentiation of the Rankine-Hugoniot equation, it only holds true on the Hugoniot. We can also write T dS as a total differential in terms of dP and d V... [Pg.16]

In the simplest case when a single shock state is achieved via a shock front, the Rankine-Hugoniot equations involve six variables U, u, p, Pi, i — Eq, and Pi) thus, measuring three, usually U, m, and p, determines the shock state, pi, , - A- The key assumption underpinning the... [Pg.77]

To demonstrate that the Rayleigh line actually represents the thermodynamic path to which material is subjected on being shocked from state p = 0, F = Fq to P = Pi, F = Fi, we demonstrate below that the shock wave sketched in Fig. 4.1 must be steady. Moreover, the Rankine Hugoniot equations ((4.1)-(4.3)) not only describe the conservation of mass, momentum. [Pg.77]

At the shock front in free air, a number of wave properties are interrelated through the Rankine-Hugoniot equations. These three equations are (Reference 5) ... [Pg.6]

The behavior of shock waves is ruled by the Rankine-Hugoniot equations, which express the conditions for conservation of mass, momentum, and energy and can be used to design suitable shock prohles. Referring to the PV diagram (see left panel of Fig. 13), the compressed state (P, V ) can be represented as... [Pg.137]

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. [Pg.11]

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-... [Pg.257]

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... [Pg.188]

Rankine-Hugoniot equation is also discussed under "Detonation, Theories of"... [Pg.279]

Up, to the pressure p and specific volume v of the compressed material. The relationships are given by the Rankine-Hugoniot Equations ... [Pg.279]

The pressure and volume of the detonation products immediately behind the detonation front are related by the third Rankine-Hugoniot equation which defines the... [Pg.291]

Pure shock waves) 4) G.B. Kistiakowsky, p 951 in Kirk Othmer 5 (1950), pp given in the text (Not included in the 2nd edition) 5) Corner, Ballistics (1950), 100-01 (Corner Noble-Abel equations of state) 6) SAC MS, Ballistics (1951), 18 (Covolume and equation of state of propint gases) 7) Taylor(1952), 34 (Boltzmann and Hirschfelder Roseveare equation of state for the expln products) 69-72 (Rankine-Hugoniot equation of state) 87-98 (Abel, Boltzmann and other equations of state applicable to deton of condensed expls yielding only gaseous products) 114 (Equations of state applicable to deton of condensed expls whose products contain a condensed phase)... [Pg.296]

CA 48, 3691(1954) (Application of Cottrell-Paterson equation of state to oxygen-deficient expls like TNT) 8b) A.K. Oppenheim, "Gasdynamic Analysis of the Development of Gaseous Detonation and Its Hydraulic Analogy , 4thSympCombstn(1953), p 472 (Hugoniot and Rankine-Hugoniot equations)... [Pg.296]

Rankine-Hugoniot equations 181-87 (Equations of state which include among others the following Jones Miller, Lennard-Jones Devonshire, Halford-Kistiakowsky-Wilson, Joffe its modification by Su Chang, Taylor, Kihara Hikita, Travers, Cook, Kistiakowsky-Wilson-Brinkley and Polytropic equations) 194 (Landau-Stanyukovich and Hirschfelder et al equations of state 11) J.F. Roth, Explosiv-stoffe 1958, 50 (Abel sche Zustandsgleichung fur die Detonation) 12) Cook (1958), 37 (General equation of state) 62-3 [Halford-Kistiakowsky-W ilson-Brinkley equation of state, (listed as K-H-W-B equation of state)] ... [Pg.297]

Detonation, Rankine-Hugoniot Equations and Rankine-Hugoniot Relation in. See under DETONATION (AND EXPLOSION), THEORIES and in paper of M.W. Evans ... [Pg.500]

This eq is the same as eq 93a listed in Ref 93, p 45 and called by.J.G. Coffin the complement of the Rankine-Hugoniot equation If the term Q is introduced as in Hugoniot equation, we obtain ... [Pg.605]

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... [Pg.610]

Equation (4.5) is known as the Rankine-Hugoniot equation. Hie symbols used in the above three equations, which are applied to. [Pg.610]

Theory of Detonation of Explosives , pp 948-60 in Kirk Othmer 5(1950). It includes Theory of shock wave (pp 949-52) Rankine-Hugoniot equation (951) Theory of stationary deton wave (952-55) Calcn of deton para-... [Pg.615]

Dunkle s Lecture at Picatinny Arsenal, 21 Nov 1955, p 3 (One-dimensional steady-state process and Rankine-Hugoniot equation) 78) Ibid, 13 Dec 1955, p 5 (Nature of shock waves) p 8 (Chapman-Jouguet point) pp 8-9 (Basic equations of deton) p 9... [Pg.616]

Dunkle s Syllabus (1957 58), 1-36 (Detonation phenomena, mathematical background) 37-60 (Initiation of shock waves formulas equations including Riemann equation, p 43 Hugoniot relations in gases, p 44 Rankine-Hugoniot equation, p 45 ... [Pg.617]

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... [Pg.506]

Evaluation of the density at the front, together with the Rankine-Hugoniot relations and the measured front velocity, determines the pressure and particle velocity there. In practice, this requires an additional assumption, which will be made throughout. Since the reaction zone is much smaller than the foil spacing, the reaction is treated as instantaneously complete within the shock transition, and the final state to which the Rankine-Hugoniot equations apply is taken to be the equilibrium state at the end of the reaction zone. No evidence of a reaction zone can be detected either in the analysis of the foil data or on the radiographs. [Pg.235]


See other pages where Rankine-Hugoniot equations is mentioned: [Pg.1959]    [Pg.11]    [Pg.77]    [Pg.11]    [Pg.44]    [Pg.260]    [Pg.260]    [Pg.278]    [Pg.291]    [Pg.533]    [Pg.605]    [Pg.605]    [Pg.615]    [Pg.616]    [Pg.9]    [Pg.44]    [Pg.260]   
See also in sourсe #XX -- [ Pg.11 ]

See also in sourсe #XX -- [ Pg.9 , Pg.44 , Pg.260 ]

See also in sourсe #XX -- [ Pg.9 , Pg.44 , Pg.260 ]

See also in sourсe #XX -- [ Pg.34 ]




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