10182

# 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.

### DETAILS

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.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.