Hi IntrepidLearner,
The problem you are dealing with here is not trivial unless you have some good software for flow of compressible fluids in networks, which I doubt an Electrical man would have in his toolbag. However, for you to be able to do an either/or analysis between piped air and your alternative solution a simple assumption makes a spreadsheet or hand calculation possible.
The reason I say it is not trivial is that you will lose a significant portion of your available pressure due to friction pressure drop between the regulator and the first 1/4" nozzle. Additionally, you will continue to lose pressure due to friction as the air flows down the pipe past all the nozzles, so that each nozzle has a lower supply pressure than the one before it. These two factors mean that you have to do a trial and error calculation, until you get a converged result.
When process engineers design manifolds like this we often "cheat". If the pressure drop down the manifold is small compared with the pressure drop through the branches (or orifices or nozzles in similar situations) you can regard the pressure in the manifold as constant at its supply pressure all along its length and then every branch calculation is identical and the problem does become trivial. To take your example of 7 off 1/4" branches on a 1/2" pipe - the first bit of pipe has 7 times the flow that a branch has, but it has only 4 times the area. This makes the pressure drop in the pipe relatively significant. As a rule-of-thumb the pressure drop decreases with the 5th power of the diameter, so a 1" pipe would have a pressure drop of 1/32 of that in the 1/2" pipe. If your manifold was 1" you could make these assumptions. Although I called this a "cheat" it does result in every branch having almost exactly the same flowrate, and this can have a process benefit.
Anyway, this is probably far more detail than you need or are interested in! Let's get to how you can actually do the calculation.
The assumption that I would propose to make the problem easily soluble in your case is to assume that the flow through each branch is identical. You really need to test this, but because the branches are relatively close together and because the flowrate (and therefore the pressure drop per foot) drops rapidly as you go along the manifold, it is reasonable in your case. Although you can probably ignore this pressure drop along the manifold between the first and last branches, you cannot ignore the pressure drop between the regulator and the first nozzle (i.e. you cannot assume each branch sees the full supply pressure)
You are now faced with a trial and error calculation to determine the pressure at the first branch. This can be done by
1. Guess a total flow from the regulator to the first branch
2. Based on this flow, calculate the pressure drop in the manifold from the regulator to the point of the first branch
3. From this pressure drop, you know the supply pressure to the branch (assumed the same for all n branches)
4. Calculate the flow per branch and multiply by the number of branches to get total flow
5. If the result from step 4 is different from the flow you used in step 2, take the average of these two and go back to step 2.
In determining the pressure drop in the branches I would take each branch as
one inlet loss,
one "thick orifice" for the bayonet connector
2' of hose
one exit loss
If you have a problem with these concepts ask your chemical or mechanical engineering colleagues for a copy of Crane Technical Publication #410. I suppose any fluids book would be OK, but the Crane book is very practically oriented.
I have had to guess some of your dimensions and temperatures, but my estimates are that in the 8 psi system you will get about 5.0 scfm per branch, and in the 2 psi system you will get about 2.6 scfm per branch. Standard conditions taken as 60 deg F and 14.7 psia.
Katmar Software
Engineering & Risk Analysis Software
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