(Source: am a university professor)
Do you live near a research university, which employs anyone working in aerospace engineering and/or fluid dynamics? Alternatively, do you ever have the occasion to visit your old university?
I'd try to set up some meetings with professors. Say that you've been working independently, based on questions that were bugging you in your undergrad days, and you'd be extremely grateful if you could discuss your work with them (at their convenience).
Resist the temptation to oversell your work. It sounds like you're claiming to understand drag better than an entire community of experts, who devote their careers to studying it. That is an extraordinarily difficult sell. If you make such a claim, whether in person or in a paper, then your conclusions are likely to be immediately dismissed -- especially at the first sign of any mistake.
Just say you have an alternative theory, and would be grateful to get the chance to discuss it (and have it critiqued) with an established expert. If you make a positive impression, then they will encourage you to publish your results, and will be happy to give you practical advice for doing so.
As a professor, I'd disagree with Nomentatus's suggestion that you should try to "offer to help professors in the area". Accepting help usually creates more effort (for them) than it saves.
It's okay to simply cold-email professors whom you don't know and ask if you could meet them. Be prepared for them to say no, or for them to not reply at all. If they do say yes, don't go in trying to establish a "relationship". The most likely outcome is that they'll say "Oh, that's interesting, you should read X, Y, and Z." Take notes, and -- if you're serious about this -- read X, Y, and Z before you request a second meeting.
In the meantime, make sure you understand why "most people believe drag is simply not possible in inviscid / incompressible flow". If you thoroughly understand the potential objections to your theory, then you might have a shot at convincing someone.
Here is a blog post, which outlines some of the hurdles you could potentially face.
http://blogs.discovermagazine.com/cosmicvariance/2007/06/19/...
In the long run, if your theory is correct, I believe you have good odds of getting it accepted. Good luck!