There was a discussion on the forums about a year ago on narrow annulae. If I remember correctly, there was a suggestion to check the text in Crane Technical Manual 410 (not just the formulae) as the formulae get somewhat "funky" for real narrow annulae. You could try doing a search here, or just go find a copy of Crane and read the section on annulae, paying attention to the text. You may not find a simple one-size-fits-all formula.
Patricia Lougheed
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This is the thread I was thinking about: thread378-336832. I don't know if it will be helpful to your situation or not as, in re-reading it, I see it was liquid not gas.
Patricia Lougheed
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This is a really good example of exactly why it is a terrible idea to post the same question multiple times. In your Compression Engineering thread (which I've asked site management to delete) I responded this morning:
See FAQ378-1142 The "petroleum method" in the FAQ has worked very well for me in the past (i.e., calculated pressure drop is very close to measured pressure drop) on bigger annular spaces, but on your scale you have a whole range of microscopic effects that I'm not sure an equivalent diameter calculation will do you much good. On your scale I'd be worried about the boundary layers of the two pipes interfering with each other.
There was an Eng-Tips thread 378-39128 which discussed annular flow and referenced work by Lenkei, and work by Bell and Bergelin published in ASME Transactions, 1956. It involved a trial and error solution using an emperical data chart relating radial clearance/flow length to a flow factor K for various Reynolds numbers.
I also found the same reference in 'Hydraulic and Pneumatic Power and Control' by Franklin Yeaple, 1966.
