I'm struggling with this question right now:(adsbygoogle = window.adsbygoogle || []).push({});

Let the complex velocity potential [itex] \Omega(z) [/itex] be defined implicitly by

[tex] z = \Omega + e^{\Omega} [/tex]

Show that this map corresponds to (some kind of fluid flow, shown in a diagram, not important).

For background,

[tex] \Omega = \Phi + i\Psi [/tex]

where Phi is the velocity potential:

[tex] \mathbf{v} = \nabla\Phi [/tex]

and Psi is the harmonic conjugate of Phi (therefore it is the streamfunction of the fluid flow.

My first thought was that I need to find the level curves of the streamfunction in order to find out what kind of flow this is. But before I can do that, I need to solve for Omega explicitly. THAT's where I'm stumped. Any suggestions on a strategy or approach?

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# Homework Help: Complex Analysis => Fluid Flow

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