Flow through an "annular orifice".
Flow through an "annular orifice".
(OP)
Greetings Mechanikals,
I need some help in determining the flow through what I will call an “annular orifice”.
1. I have a smooth pipe with an inside diameter of 24 in.
2. Centered in that pipe is a thin plate with an outside diameter that is 0.08 in. smaller than the inside diameter of the pipe.
3. I know the pressure drop across the plate to be 0.5 psid.
4. The medium is water at 80 deg F.
What is the formula for calculating the flow through this annulus?
Thanks in advance,
Goosen
I need some help in determining the flow through what I will call an “annular orifice”.
1. I have a smooth pipe with an inside diameter of 24 in.
2. Centered in that pipe is a thin plate with an outside diameter that is 0.08 in. smaller than the inside diameter of the pipe.
3. I know the pressure drop across the plate to be 0.5 psid.
4. The medium is water at 80 deg F.
What is the formula for calculating the flow through this annulus?
Thanks in advance,
Goosen





RE: Flow through an "annular orifice".
RE: Flow through an "annular orifice".
Goosen
RE: Flow through an "annular orifice".
No, you will have to consider it as an annulus, you are right. Unfortunately, I don't have the time to look it in my Fluids book, but any advanced fluid mechanics text will have that, it's fundumental to training engineers since it's such an interesting flow problem.
BobPE
RE: Flow through an "annular orifice".
RE: Flow through an "annular orifice".
I only have my undergraduate Fluids text and it does not address this problem. That is why I am here seeking the expertise of this gathered assembly.
Goosen
RE: Flow through an "annular orifice".
You might turn the annular area into an equivilent diameter [((ID+OD)^2)*(ID-OD)^3]^(1/5)] and use orifice calcs, but I wouldn't have a lot of faith in the answer.
RE: Flow through an "annular orifice".
RE: Flow through an "annular orifice".
The annular flow problem simplified for industrial applications can be found in the following classic reference:
Process Heat Transfer by Donald Q. Kern
Chapter 6, Counterflow: Double Pipe Heat Exchangers
The whole chapter deals with Heat Transfer and Pressure drop in annular flow...
In your case, being the OD of the internal plate only 0.08in smaller than the ID of the 24in pipe you may have laminar flow... which is a whole different story.
HTH
Saludos.
a.
RE: Flow through an "annular orifice".
Simple problem. You estimate the free area, assume a discharge coefficient, and calculate the flow. It is only an estimate, but it is actually pretty good.
Most flow or mechanical engineering handbooks have all the information you'll need.
RE: Flow through an "annular orifice".
Thank you for the references. I will investigate them. I also appreciate your time spent iterating with the spreadsheet. Please let me know if you can confirm the sample problem results.
Hacksaw,
I tried the approach that you recommend early on and I have difficulty accepting the results. That is, the flow seems higher than I would expect. That is not to say that it is not approximately correct, only that the result caused me to pause and wonder if this problem, with the very small annulus width-to-diameter ratio did not call for some other approach. I found other formulations with regard to annular flow, of the inner and outer pipe (very unlike an orifice) and 2. the annulus width-to-diameter ratios were not nearly as small. The results from these equations were even more unrealistic. This is truly an "annular orifice" problem.
Goosen
RE: Flow through an "annular orifice".
I left out some text in my response. It should have said,
****************
Hacksaw,
I tried the approach that you recommend early on and I have difficulty accepting the results. That is, the flow seems higher than I would expect. That is not to say that it is not approximately correct, only that the result caused me to pause and wonder if this problem, with the very small annulus width-to-diameter ratio did not call for some other approach. I found other formulations with regard to annular flow, *where 1. there was relative significant length* of the inner and outer pipe (very unlike an orifice) and 2. the annulus width-to-diameter ratios were not nearly as small. The results from these equations were even more unrealistic. This is truly an "annular orifice" problem.
Goosen
RE: Flow through an "annular orifice".
RE: Flow through an "annular orifice".
RE: Flow through an "annular orifice".
RE: Flow through an "annular orifice".
Thanks again for your efforts, vanstoja, I really appreciate the help.
Goosen
RE: Flow through an "annular orifice".
At your c/l of 0.667, the curve shows all Reynolds numbers from 500 to 20,000 bunched around K=0.71. Your Re is 4518.296 which would be turbulent.
Good news or bad news?
RE: Flow through an "annular orifice".
A colleague did a simple CFD analysis and your result comports well with what he found.
It is somewhat "bad news" in that we were hoping the leakage would be much less than this, but "the facts is the facts", as they say, and THAT is why I like practicing engineering.
Thanks again for your time and efforts.
Goosen
RE: Flow through an "annular orifice".
I'm interested in knowing of the references you found that would help calculate/estimate capacity loss of gas flow through a pipe into which a smaller pipe (d/D < .25) is inserted. In other words annular flow outside of innerpipe. Thanks!
RE: Flow through an "annular orifice".
The calculation is commonly used in estimating the leakage flows for large (swing-thru) dampers and butterfly valving, etc.
If the gap is greater than the thickness of the plate, then you can use the thin restriction discharge coefficient, if the thickness is comparable to or greater than the gap, you have to assume what is known as a thick plate restriction.
The real problem is not your fluids calculation, but your ability to confirm the annular gap.With 0.5 psid on a thin plate you will actually bend the plate unless it is re-inforced, and the leakage will be much greater.
Differential thermal expansion is also an issue. Even a 10 deg difference between shop and service conditions will cause a considerable difference in the calc. flow.
Back to the flow calc. All flow calc. are based on the bernoulli equation (ultimately). You only have to sort out the discharge coeff. based on hydraulic similarity, and the hydraulic radius of the flow channel.
good luck,
Valve
RE: Flow through an "annular orifice".
I realize this is an old thread but thought I'd offer another source of reference for this application.
R.W. Miller's Flow Measurement Engineering Handbook, 2nd Ed
pp. 11-5 through 11-7 discusses the Annular Orifice and gives an example.
bk
RE: Flow through an "annular orifice".
Can someone post the equations or a link to them?
Thanks!!!!
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