Read e-book online Introductory Fluid Mechanics for Physicists and PDF

By Pert, Geoffrey

ISBN-10: 1299315925

ISBN-13: 9781299315921

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Extra resources for Introductory Fluid Mechanics for Physicists and Mathematicians

Sample text

If this requirement is violated the loop is broken as one part goes along one side of the surface and the other part along the other. Kelvin’s theorem therefore no longer holds. This streamline thus separates the region of zero vorticity from one where the vorticity may be finite. As a consequence a tangential discontinuity may form along the streamline, across which the tangential component of velocity changes discontinuously, but the pressure and normal velocity component are continuous. The discontinuity itself forms a ‘vortex sheet’ due to the velocity difference, which is equivalent to an infinitely thin layer of vortices of appropriate strength per unit area.

G. aerofoils. In this case the problem of non-uniqueness is resolved by an additional empirical condition, which frequently allows accurate representations of the flow found in practice. Introductory Fluid Mechanics for Physicists and Mathematicians, First Edition. Geoffrey J. Pert. © 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. 25 26 Introductory Fluid Mechanics Much of the theory of aerodynamics in consequence has been constructed around inviscid flow models. 2. Waves and instabilities.

41) shows that the inclusion of the additional term ∂φ/∂t yields a form which is time dependent and valid throughout the flow, not just along a streamline, but is only applicable in irrotational flow. 33 Flow of Ideal Fluids Since v · d increases along a streamline, it follows from Stokes’ theorem that, if the potential is single valued (acyclic flow ),4 the streamlines must start and finish on the surface of a body or at infinity. 12) since ∇φ = v is parallel to the streamline δ , unless the flow velocity is zero and the potential constant.

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Introductory Fluid Mechanics for Physicists and Mathematicians by Pert, Geoffrey


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