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Fluid Dynamics: Part 1: Classical Fluid Dynamics

Anatoly I. Ruban and Jitesh S. B. Gajjar

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199681730
eISBN:
9780191761607
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199681730.001.0001
Subject:
Physics, Soft Matter / Biological Physics

This book, the first of a four-part series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum ... More


Fluid Mechanics: A Geometrical Point of View

S. G. Rajeev

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.001.0001
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using ... More


Geometric Integrators

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0015
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Generic methods for solving ordinary differential equations (ODEs, e.g., Runge-Kutta) can break the symmetries that a particular equation might have. Lie theory can be used to get Geometric ... More


Inviscid Incompressible Flows

Anatoly I. Ruban and Jitesh S. B. Gajjar

in Fluid Dynamics: Part 1: Classical Fluid Dynamics

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199681730
eISBN:
9780191761607
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199681730.003.0004
Subject:
Physics, Soft Matter / Biological Physics

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 ... More


Bernoulli’s equation

Marcel Escudier

in Introduction to Engineering Fluid Mechanics

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198719878
eISBN:
9780191840180
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198719878.003.0007
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

In this chapter Newton’s second law of motion is used to derive Euler’s equation for the flow of an inviscid fluid along a streamline. For a fluid of constant density ρ‎ Euler’s equation can be ... More


Euler’s Equations

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0002
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the ... More


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