Pressure field of an irrotational vortex

AI Thread Summary
The discussion centers on determining the pressure field of an irrotational vortex characterized by a velocity profile of v_theta = 1/r and v_r = 0. It highlights that while the Bernoulli equation applies to streamlines, the velocity remains constant along the vortex's streamlines, leading to a pressure difference between adjacent streamlines. The conversation notes that a suction force will act on finite-sized objects toward the axis of rotation due to this pressure difference. Additionally, it suggests using a force balance approach, equating the centrifugal force on a fluid element with the pressure force, to analyze the pressure changes. Understanding these dynamics is crucial for accurately describing the behavior of irrotational vortices.
mikeph
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time for some revision... I can't find any definitive verification for this

I'm trying to find the pressure field of an irrotational vortex, v_theta = 1/r, v_r = 0; I guess the pressure falls but I'm not sure how since the Bernoulli equation constant only holds over streamlines, and over streamlines of the vortex, velocity is constant!

Thanks for any help
 
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There will be a pressure difference between adjacent streamlines. On any finite sized object there will be a suction force drawing the object toward the axis of rotation.
 
If the flow is inviscid then the total pressure is the same everywhere so you can use Bernoulli to find the change in pressure across streamlines.

You could also determine this change in pressure by doing a force balance in the direction perpendicular to the motion. Balance the centrifugal force on the fluid element with the pressure force.
 

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