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Fluid DynamicsPart 1: Classical Fluid Dynamics$
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Anatoly I. Ruban and Jitesh S. B. Gajjar

Print publication date: 2014

Print ISBN-13: 9780199681730

Published to Oxford Scholarship Online: August 2014

DOI: 10.1093/acprof:oso/9780199681730.001.0001

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Elements of Gasdynamics

Elements of Gasdynamics

Chapter:
(p.233) 4 Elements of Gasdynamics
Source:
Fluid Dynamics
Author(s):

Anatoly I. Ruban

Jitesh S. B. Gajjar

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199681730.003.0005

This chapter deals with inviscid compressible flows of a perfect gas. It starts with an analysis of small perturbations propagating through a gas at rest using piston theory and then turns to integrals of motion, including compressible versions of the Bernoulli equation, entropy conservation law, and Kelvin’s Circulation Theorem. Crocco’s formula, which allows determination of whether a flow is potential in the presence of shock waves, is derived. The theory of characteristics is formulated for two-dimensional potential flows and applied to Prandtl–Meyer flow over a body surface bend and flow past a corner. The formation of shock waves, normal or oblique, is discussed. The shock conditions are deduced and the shock polar, which describes the behaviour of oblique shocks, is introduced. These results are applied to flows past a wedge and a circular cone. Finally, unsteady compressible flows are analysed, in particular shock tubes and blast waves are considered.

Keywords:   piston theory, Crocco’s formula, theory of characteristics, Prandtl–Meyer flow, shock wave, shock polar, shock tube, blast wave

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