Looking for formula...if it exists 1

[ajr23]

Trying to design a pneumatic system. System is a length of pipe/tubing with several holes in the tube. Knowns are ID of tube, source pressure, hole diameter, spacing of holes, length of tube, source cfm rate and all knowns are mostly adjustable. Would like a formula to determine the pressure and cfm rate at each hole with the knowns. Example, a .50 inch ID tube, 22 feet long, 5 holes @ .063 diameter spaced 5 feet apart with 1 foot at the ends, end of tube is capped, source pressure 200 psi and 10 cfm. System is at atmospheric normally, until valve opens and releases source pressure and cfm into tube creating 5 air jets from tube.

Thanks,
mcs

 

[m777182]

If you have an empirical relationship- an empirical formula or a model in mind you can construct it yourself but you need a lot of experimental data. It is important that your data points cover the entira range of your possible interes as much equally spaced as possible. In Excel you put your data in columns and try to fit a simple model with Analysis Tool- regression.
A better way is to start with a designed experiment; you will need less experimental points and will get a better model more efficiently.
m777182

 

[katmar]

The system you have described is over specified. You cannot specify the source pressure and flow, plus the pipe geometry. One of those three factors has to be dependent on the other two.

I do not believe it is feasible to try to create a single formula to do this, unless you make a LOT of simplifying assumptions. This is because the nature of the relationships between the factors necessitates a trial-and-error solution.

The easiest way to solve it would be to model it with some pipe network software. If you do not have access to this software, you could probably build a model fairly easily in a spreadsheet, as the formulas would be very repetitive. Using a "goal seeking" function in the spreadsheet would force it to iterate and perform the trial-and-error solution.

Having said all this, it is relatively easy to design sparger systems by simply designing the pipework such that the pressure drop through the pipe is negligible compared with that through the holes. (Apologies to the members who have heard me say this so often before.) With this proviso, the spacing of the holes becomes irrelevant, and the problem becomes a simple design of n identical orifice holes - i.e. the whole bang-shoot resolves itself into one orifice calculation.

regards
katmar

 

[athomas236]

If you design the pipe as basically frictionless (or nearly) what happens after the gas has passed one take-off, so the velocity after the take off is lower than that before. Does this slow down create an increase in pressure in accrdance with Bernouli's theory.

Just a thought.

Regards,

athomas236

 

[ajr23]

Thanks all. I was planning on doing several experiments to get data, holding a few items fixed and vary others. Probably will have to do a simple regression model to get me in the correct direction.

I was just hoping someone might have done something like this before.

Thanks,
mcs

 

[katmar]

Hi athomas236,

I suppose that theoretically it is correct that the lower velocity would give a higher static pressure, but the velocities are much too low to have any perceptable effect.

katmar

 

[israelkk]

Since the tube section area is 12.6 times larger than the 5 0.063" diameter holes we can practically assume that the whole tube is basically a pressure vessel with a constant pressure of 200 psi.

Assuming a discharge coefficient of 0.9 for each drilled hole the flow rate will be 16.3 cfm from each hole. The variations between each hole flow rate will probably will be due the variations in the discharge coefficient and the hole diameter tolerances and not the distance between the holes.

 

[israelkk]

I assumed 200 psia.

After looking again at the first post, I noticed that the flow supply is 10 cfm which is less that the 16.3 cfm if I assume 200 psi inside the tube. Therefore my calculations are not valid and the tube should be taken as an added resistance to the 5 063" holes.

 

[vzeos]

Ajr23,

What you are describing seems similar to a radial distribution gas main, i.e. a long dead end pipe with loads taken off along the way. In this case, the flow through the pipe is not the source capacity; it is the sum of the loads. The total flow (QT) is the sum of the flows through the 0.063 holes (Q1+Q2+Q3+Q4+Q5). Since your source pressure is 200 psi I would assume that the flow in each 0.063 hole is critical, constant and knowable.

The way to approach this problem is to divide the length into segments; L1, L2 … and assign nodes (Ni) to each Qi. Then L1 is the length from the source (S) to N1 where Q1 is taken off as a load. The source pressure (PS=200 psi) is assumed set. P1 can be found by calculating the pressure drop over L1. The load to apply to find P1 is QT. Next, L2 is the distance from N1 to N2. The initial pressure for this segment is P1. The load to apply to find the P2 is QT-Q1. Next, L3 is the distance from N2 to N3. The initial pressure for this segment is P2. The load to apply to find the P3 is QT-Q1-Q2. Repeat the process until you have the pressure at each hole.

I hope this accurately describes your problem and helps in its solution.