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Fluid MechanicsA Geometrical Point of View$
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S. G. Rajeev

Print publication date: 2018

Print ISBN-13: 9780198805021

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198805021.001.0001

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Ideal Fluid Flows

Ideal Fluid Flows

(p.45) 4 Ideal Fluid Flows
Fluid Mechanics

S. G. Rajeev

Oxford University Press

Some solutions of Euler’s equations are found here. The simplest are the steady flows: water flowing out of a tank at a constant rate, the Venturi and Pitot tubes. Another is the static solution of a self-gravitating fluid of variable density (e.g., a star). If the total mass is too large, such a star can collapse (Chandrasekhar limit). If the flow is both irrotational and incompressible, it must satisfy Laplace’s equation. Complex analysismethods can be used to solve for the flow past a cylinder or inside a disk with a stirrer. Joukowski used conformal transformations on the cylinder to find the lift of the wing of an airplane, in the limit of zero viscosity. Waves on the surface of a fluid are studied as another example. The speed of these waves is derived as a function of their wavelength and the depth of the fluid.

Keywords:   Venturi tube, Pitot tube, self-gravitating fluid, Chandrasekhar limit, Laplace’s equation, conformal transformation, Joukowski airfoil, surface waves, dispersion relation

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