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FLUID MECHANICS - CASE STUDY

    Introduction


Free Vortex
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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:

     vr = 0    and    vθ = 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.