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Inviscid flow past a stationary sphere

This notebook has been written in *Mathematica *by

Mark J. McCready

Professor and Chair of Chemical Engineering

University of Notre Dame

Notre Dame IN 46556

USA

Mark.J.McCready.1@nd.edu

http://www.nd.edu/~mjm/

It is copyrighted to the extent allowed by whatever laws pertain to the World Wide Web and the Internet.

I would hope that as a professional courtesy, that this notice remain visible to other users.

There is no charge for copying and dissemination

Version: 6/18/00

More recent versions of this notebook should be available at the web site:

http://www.nd.edu/~mjm/InviscidSphere.nb

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Reference: M. M. Denn, Process Fluid Dynamics, Prentice Hall, 1978

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Summary

This notebook considers the problem of an inviscid flow past a stationary sphere. Solutions are obtained using both a potential function and a stream function. The pressure field around the sphere and the drag, which is 0 (d'Alembert's paradox) are found.

This solution is a nice example of how for an inviscid flow (the idealized limit of a very high Reynolds number flow), the flow field can be computed even though the governing Euler equations are nonlinear. This is because the flow can be considered irrotational (vorticity=0) so that the flow field can be defined as the gradient of a scalar potential function.

Such a formulation should give useful results for high reynolds number flows away from boundaries where vorticity is produced. Perhaps the best example of the utility of inviscid flow theory is for flow around airfoils to give the pressure field and thus the lift. The drag is obtained from boundary-layer theory -- where viscous effects are important.

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*Mathematica* aside

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Keywords

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Homework questions for this notebook:

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Problem statement

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Solution using the velocity potential

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Solution using the stream function

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Pressure distribution

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Other issues

Converted by *Mathematica*
June 18, 2000