Conditions Across the Shock: The Rankine-Hugoniot Equations

  • Seán Prunty
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)


This chapter deals with the Rankine-Hugoniot relations connecting the states on both sides of a shock wave. These relationships are shown to produce important formulae connecting the pressure, density and temperature ratios on either side of the shock surface. In addition, other useful relationships are derived and presented in terms of the Mach number and the limiting form of these relationships in the case of weak and very strong shocks is discussed. The increase in the entropy of a gas on its passage through a shock is also considered. Finally, the reflection of a plane shock from a rigid plane surface is discussed and a relationship connecting the Mach numbers of the incident and reflected shocks is presented.


Rankine-Hugoniot equations Normal shock waves Mach number Strong shocks Entropy increase across a shock Reflected shock 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Seán Prunty
    • 1
  1. 1.BallincolligIreland

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