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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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Fundamentals of Fluid Dynamics

Fundamentals of Fluid Dynamics

(p.4) 1 Fundamentals of Fluid Dynamics
Fluid Dynamics

Anatoly I. Ruban

Jitesh S. B. Gajjar

Oxford University Press

This chapter starts with a discussion of the continuum hypothesis and the conditions under which it can be used. The origin of the internal forces acting in moving fluids is then identified and the notion of the surface stress and the stress tensor are introduced, as is the rate-of-strain tensor. The constitutive equation, which relates the surface stress to the deformational motion of a fluid, is then derived. Newton’s Second Law and the law of conservation of energy are applied to deduce the equations governing fluid motion. These are known as the Navier–Stokes equations. They are derived for both incompressible fluid flows and compressible flows of a perfect gas. The chapter concludes with a demonstration of how the Navier–Stokes equations can be expressed in curvilinear coordinates.

Keywords:   continuum hypothesis, stress tensor, rate-of-strain tensor, constitutive equation, Navier–Stokes equations, curvilinear coordinates

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