The complex potential of a line vortex of strength k centred on the origin is W=iklnz. Determine the complex potential of two line vortices of the same strength k , one located at the origin and one located at the point (x0,y0) . Show that at large distances, r≫r0=x20+y20‾‾‾‾‾‾‾√ , it reduces to the complex potential of a single vortex of strength 2k .
The complex potential of a line vortex of strength k centred on the origin is W=iklnz. Determine the complex potential of two line vortices of the same strength k , one located at the origin and one located at the point (x0,y0) . Show that at large distances, r≫r0=x20+y20‾‾‾‾‾‾‾√ , it reduces to the complex potential of a single vortex of strength 2k .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The complex potential of a line vortex of strength k centred on the origin is W=iklnz. Determine the complex potential of two line vortices of the same strength k , one located at the origin and one located at the point (x0,y0) . Show that at large distances, r≫r0=x20+y20‾‾‾‾‾‾‾√ , it reduces to the complex potential of a single vortex of strength 2k .
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