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Radius of a vortex

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BlackGarden | 20:50 Thu 30th Sep 2004 | How it Works
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This is a fairly random question but I've been digging around various internet sites for ages and I'm starting to lose my sanity. Does anybody here just happen to know of an equation relating the radius of a vortex formed in a fluid to its height? Or even where the radius of the vortex is measured? Thanks in advance.
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The vortex will be a different depth depending on how fast the liquid is escaping down the pipe/tube

 The faster it escapes the deeper the vortex will be from it's height and the slower it escapes the vortex will be nearer it's height.

The vortex should always be in the middle of the pipe.

I am not qualified to answer this question but these are observations I have witnessed in 35 years of work in the  petrochemical industry

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