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

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Version:  6/18/00
More recent versions of this notebook should be available at the web site:

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


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.       

Mathematica aside


Homework questions for this notebook:

Problem statement

Solution using the velocity potential

Solution using the stream function

Pressure distribution

Other issues

Converted by Mathematica      June 18, 2000