Tom was told that a steady free vortex is considered one type of irrotational flow. However, he is not convinced, and he would like to prove it mathematically. The velocity components of a two-dimensional free vortex are given by:

v_{r} = 0 and v_{θ} = K/r

where K is a constant and represents the strength of the vortex.

Questions

Show that the vorticity of the free vortex is zero. Find the velocity potential associated with the free vortex.

Approach

Use polar coordinate system in the analysis.

Assume the flow is steady.

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