# Steady Flow over a Rotating Disk: von Kármán Swirling Flow

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The steady flow induced by a infinite disk that rotates in its own plane at is a classical problem in fluid mechanics. It is one of the few examples of a viscous flow that involves all three components of velocity and admits an exact solution to the Navier–Stokes equations. The velocity field for the swirling flow is given by: . The Navier–Stokes equations reduce to:

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Contributed by: Brian G. Higgins and Housam Binous (June 2011)

Open content licensed under CC BY-NC-SA

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References

[1] F. M. White, *Viscous Fluid Flow*, New York: McGraw–Hill, 1974.

[2] G. K. Batchelor, *An Introduction to Fluid Dynamics,* Cambridge: Cambridge University Press, 1967.

[3] H. Schlichting, *Boundary-Layer Theory*, 6th ed., New York: McGraw–Hill, 1968.

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