Gas Dynamics

  • Kolumban HutterEmail author
  • Yongqi Wang
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


This chapter on gas dynamics illustrates a technically important example of a fluid field theory, where the information deduced by the second law of thermodynamics delivers important properties, expressed e.g. by the thermal and caloric equations of state of, say, ideal and real gases. Problems of acoustics, steady isentropic flow processes and their stream filament theory are briefly touched. The description of the propagation of small perturbations in a gas serves in its one-dimensional form ideally as a model for the propagation of sound e.g. in a flute or organ pipe, and it can be used to explain the Doppler shift occurring when the sound source is moving relative to the receiver. Moreover, with the stream filament theory, the sub- and supersonic flow through a nozzle can be explained. In a final section the three dimensional theory of shocks is derived as the set of jump conditions on surfaces for the balance laws of mass, momentum, energy and entropy. Their exploitation is illustrated for steady surfaces for simple fluids under adiabatic flow conditions. This leads to the well-known RankineHugoniot relations. These problems are classics; gas dynamics, indeed forms an important advanced technical field that was developed in the 20th century as a subject of aerodynamics and astronautics and important specialties of mechanical engineering.


Acoustic waves Generation of sounds D’Alembert’s and Bernoulli’s solution Acoustic Doppler effect Isentropic stream filament theory Laval nozzle Theory of shocks Stationary shocks RankineHugoniot relations 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.c/o Versuchsanstalt für Wasserbau, Hydrologie und GlaziologieETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

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