Potential Flows

A potential flow is characterized by a velocity field that is the gradient of a scalar function, the velocity potential. This velocity field is irrotational, because the curl of a gradient is identically zero. Velocity potentials are obtained as solutions of Laplace's equation, most conveniently in the complex plane. Some applications include water-wave propagation, airfoils, electrostatics, and heat flow. The equations can be used for modeling both stationary and nonstationary flows.
Potential flows for different cases are shown. As described in the references, is the velocity field and is the strength of the source, while , , , , , and are other hydrodynamic parameters in the model.

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References
[1] B. J. Cantwell. "Elements of Potential Flow, Chapter 10, AA200: Applied Aerodynamics." (Apr 6, 2014) http://web.stanford.edu/~cantwell/AA200_Course_Material/AA200_Course_Notes/AA200_Ch_ 10_Elements _of _potential _flow _Cantwell.pdf.
[2] P. Nylander. "Potential Flow." (Aug 4, 2014) bugman123.com/GANNAA/index.html.
[3] J. H. Mathews. "Complex Analysis Project." (Aug 4, 2014) mathfaculty.fullerton.edu/mathews/complex.html.
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