# Pressure to volume relationship in compressed air

1. Nov 11, 2013

### chot

Hi guys need help.

We've been encountering compressed dry-air related problems here in our plant. Most machines
pressures were fluctuating when their equipments are running. As I've checked, the problem is not
regarding the pressure since the line pressure is 10psi higher than machine requirement. That's why I started to get data regarding their machines' flowrate requirement. To my surprise, the flowrate being supplied by the coupler is 18cfm which is only 1/2 of the total cfm that can be provided by our existing 8mm (ID) PUR hose- 38 to 45cfm. Machines' flowrate requirement (peak) is 30-34cfm. That's why I'm having a study on the possible standardization of all the cda coupler.
My question is what formula can I use to justify that by having a larger coupler (ID) will not only increase the flowrate but also the pressure as well - this is base on actual as 2 different machines' pressure went 4 and 10 psi higher upon increasing their volume which is contradicting the Ideal gas law- P1V1=P2V2, with constant temperature.

2. Nov 11, 2013

You can't really assume constant temperature here though since you have an expanding gas. You are better off assuming it is adiabatic, so the ideal gas law would yield $p = \rho R T$, or more like your form,
$$\dfrac{p_1}{\rho_1 T_1} = \dfrac{p_2}{\rho_2 T_2}.$$

I think what you are basically describing is that you have a constant line pressure in your compressed air line and it wasn't supplying enough air to the machines, so by increasing the supply pipe diameter (or at least that of the coupler) you noticed that the machines were getting more air, including a noticeable rise in pressure inside the machine. Is this correct?

Last edited: Nov 11, 2013
3. Nov 14, 2013

### chot

exactly bro.

4. Nov 18, 2013

### Baluncore

Rather than replacing the air lines with lines of greater capacity, you could simply add a local reservoir tank at only those machines that have significantly alternating changes in their air requirements.

5. Nov 18, 2013

Without knowing the pressures everywhere it would be hard to come up with the right equations, but basically what is happening is that the mass flow rate through an orifice (in this example, the pipe coupler) is dependent on, among other things, the diameter of the orifice. Since you increased that diameter, it increased the flow rate.

Previously, the machine was probably using up air at a rate that would only allow the reservoir in the machine to some relatively small tank pressure because the air line simply couldn't supply enough air to fill the tank further. When the mass flow rate into the machine was increased, the reservoir in the machine was able to fill more completely and so registered a higher pressure.

6. Nov 18, 2013

### heyland

baluncore is right, we have use reservoir tank which fix are feed pressures and flow at the machines, p.s. you will have to drain those reservoir.

7. Nov 18, 2013

### Baluncore

I mount the reservoir with the opening at the bottom so water can not collect in the reservoir. Gas cylinders make good reservoirs. A big 'T' connector and airline connects the reservoir to the machine.

8. Nov 18, 2013

Using a reservoir would certainly help, but you must still take into account the internal diameter of all pipes and fittings, otherwise you may either simply drain your reservoir much faster than it can refill (which may or may not be an issue depending on how long the machine must be running), or else you could choke the flow coming from the reservoir and run into the same problem you had in the first place.

9. Nov 22, 2013

### chot

Actually bro this is one of the options that I had in mind, however it will only answer the problem for those equipment with heavy flow rate requirement and is not cost-efficient/effective since we have at least 300+ equipment with high volume requirement running at a give time.

Basing on the evaluation result that I've made, increasing the orifice diameter of the coupler
will not only provide higher flowrate (x2) or almost zeroing out the drop in flow rate but as well zeroing out the pressure drop from the supply. Case in point --- The pressure from main line is 80psi (this is common at all lines since the CDA line is looped and we have transducers connected to our BMS) and the flowrate is 48cfm (from 9mm ID existing Polyurethane hose). When using the 5mm inch ID swagelok (coupler) the pressure is down to 65-70psi and flowrate to 18-22cfm.

I used a 10mm ID Swagelok and pressure registered to 78psi and the flowrate is equal to 45cfm.
Since we are operating at 70psi (equipment), I find it as an Enercon opportunity to decrease the setpoint in our Variable speed drive compressors. This case is evident for 3 manufacturing equipment.

With such, I'm doing a study and likewise can't
come up with the correct formula or equation that can "theoretically" solidify my claims above (cause using the ideal gas law will actually contradicts it).

10. Nov 22, 2013

### chot

sorry for the mess-up, but the reservoir I'm referring to actually is the filter housing which will act as the reservoir for the equipment since adding reservoir tank at manufacturing line is a no-no due to safety issues...

:)

11. Nov 22, 2013

### Baluncore

If you can demonstrate that the couplers are significantly obstructing the flow then you need to upsize them even if you cannot find an appropriate theoretical solution. No doubt you have been here...
https://en.wikipedia.org/wiki/Orifice_plate#Flow_of_gases_through_an_orifice

My suggestion to use local reservoirs is only applicable to machines that need much air suddenly and then little for the rest of the cycle. It reduces the need for replacing air lines, also the fluctuations do not upset other eqiuipment so much.

12. Nov 22, 2013

### chot

no bro, i was not able to check that one.
thanks by the way for the link anyway...

:D