Extension of the Circle Theorems by Surface Source Distribution

[+] Author and Article Information
O. Rand

Technion—Israel Institute of Technology, Haifa 32000, Israel

J. Fluids Eng 111(3), 243-247 (Sep 01, 1989) (5 pages) doi:10.1115/1.3243637 History: Received April 04, 1988; Online October 26, 2009


The paper presents a closed-form analytical solution for the source strength distribution along the circumference of a two-dimensional circular cylinder that is required for producing an arbitrary distribution of normal velocity. Being suitable to be used with flows having arbitrary vorticity distribution, the present formulation can be considered as an alternative and extensive form of the circle theorems. Using the conformal transformation technique, the formulation also serves as a closed-form solution of Laplace’s equation in any two-dimensional flow domain that is reducible to the outer or inner region of a circular cylinder having arbitrary prescribed normal velocity over its boundary.

Copyright © 1989 by ASME
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