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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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Inviscid Incompressible Flows

Inviscid Incompressible Flows

Chapter:
(p.129) 3 Inviscid Incompressible Flows
Source:
Fluid Dynamics
Author(s):

Anatoly I. Ruban

Jitesh S. B. Gajjar

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199681730.003.0004

This chapter starts by formulating the Euler equations and the boundary condition for inviscid flow, namely the impermeability condition on a rigid-body surface. The Bernoulli integral for incompressible flows is derived, as is the Cauchy–Lagrange integral, and Kelvin’s Circulation Theorem is proved. This theorem is used to identify situations where a flow can be treated as potential. Two examples of three-dimensional potential flows are considered: flow past a motionless sphere and flow produced by a sphere moving through stagnant fluid. In this chapter, attention is principally paid to two-dimensional potential flows, for which the flow analysis reduces to finding a suitable analytic function as the complex potential in the complex plane. The method of conformal mapping is discussed in detail and is used to analyse a number of flows, including flows past Joukovskii aerofoils. The chapter concludes by describing Kirchhoff flow, for which purpose free-streamline theory is used.

Keywords:   Euler equations, Bernoulli integral, Kelvin’s Circulation Theorem, complex potential, Joukovskii aerofoils, free-streamline theory

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