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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

(p.129) 3 Inviscid Incompressible Flows
Fluid Dynamics

Anatoly I. Ruban

Jitesh S. B. Gajjar

Oxford University Press

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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