Air Flow Through a Perforated Bar

[AHayden]

Good Morning All!

I have a bar (OD: 3.75", ID: 3", Length: 5') with 243 total perforation holes (Dia: 0.094") running air through to create a turn bar for a paper web to rotate over. I have attached my model. I have found the cushion pressure to be 1.143psi. This was found using PC=T/R where T is the tension of the paper and R representing the outside turn radius.

I need to find the air flow rate through the bar. I have a pressure of 2 psi inside the bar which would be enough to support the cushion pressure.

Questions have come up talking about covered vs non-covered holes. Sometimes not all the holes are covered (like when you run half a web on the bar...half of the holes are covered). I have looked at orifice equations but I haven't really found anything with perforations since the flow is perpendicular to the hole openings...

If anyone has any sources I can look at, please send them my way. Thanks!

 

[MikeHalloran]

I think this would be a good time to read up on how hydrostatic bearings work.

I suspect you will end up with a higher manifold pressure inside the bar, and stepped holes, say .094" for most of the thickness, and something like .010" through.

... to support the two situations you have to deal with.

Each uncovered hole is then basically a .010" (the number you need may be different; I am just guessing here) orifice between the manifold and the atmosphere (ignoring the contribution of the much larger counterbore). The small hole's job is to limit the flow you waste when the hole is uncovered by a web.

... and to regulate the pressure in the large hole, which supports the web.

Each covered hole is then two orifices in series: the .010" (or whatever) to a small intermediate chamber formed by the counterbore, and a second annular orifice whose area is the product of the .094" hole's circumference and the gap maintained between the paper and the bar. The gap is of course unknown at first, but you can find it iteratively, eventually.



Mike Halloran
Pembroke Pines, FL, USA

 

[AHayden]

Excellent. So I have found the flow for each hole. Now do I multiply by the number of holes to get the total flow rate inside the bar? I'm not sure how much lost there will be since the flow is perpendicular to the orifices. Maybe I can make the assumption of uniform flow and ignore the losses since the bar will always be full of air. Thoughts?

 

[MikeHalloran]

Do not be confused by the flow direction.
You are working with a fluid that goes wherever it can go, and at the pressures you assume, kinetic effects associated with its mass will be negligible.

I'm not sure how you came up with a fixed flow number at this point, but yes, you just add the per-hole flows to get the total.

Given where you are now, you might be better off to make a physical prototype a few holes wide, and run some paper tape over it and make some measurements. Are you equipped to do that? Is there an existing 'old style' machine you can use and experiment with?





Mike Halloran
Pembroke Pines, FL, USA

 

[AHayden]

We have no resources here to make a prototype. I calculated the flow based on when all the holes are uncovered. I have the pressure difference so I used equations similar to the ones here:

http://www.flowmeterdirectory.com/flowmeter_orifice_calc.html

Found a Q per hole and just multiplied by the quantity. This doesn't need to be a perfect value, just a ballpark estimate. I'm stuck on the Q now. For the blowers we are ordering, it needs to be in SCFM. I think what I calculated was found to be in ACFM...?

 

[IRstuff]

It's already been mentioned that pressure differentials drive flow. Therefore, you cannot assume that your pipe interior is at a constant pressure, since a constant pressure means no flow. You have a 5' pipe, so it's unlikely that that the flow in the first hole is going to be identical to the flow in the last hole.

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[TD2K]

The total area of your holes (243, 0.094" diameter) is about 1.69 in2. The cross sectional area of the pipe is 7.0 ft/sec. You can check the pressure drop over the 5' length to see if the dp is significant but my guess is it won't be.

 

[Latexman]

This may be a good time to do some research on "flow maldistribution".

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529