# Calculating cubic ft/ min and PSI

• johnnyShopOwner
In summary: If the air temperature is same before and after compression (you can consider the temperature after aftercooler) then the equation is much simplified to ACFM = SCFM*(Pstd/P1)">The equation would be the same regardless of the temperature, as long as the pressures are the same.

#### johnnyShopOwner

Has anyone shopped for an air compressor lately?

It's amazing how far retailers will go in providing exaggerated/skewd/completely misleading info on these things. Due to this, I have a question:

-Is there a simple formula for working with cubic feet per minute (cfm) and PSI?

Ex: If you know that a certain compressor delivers 25 cfm @ 175 psi, would it be possible to determine what the cfm would be @ 90 psi?

...or are there other factors involved which prevent such a simple formula?

Thank you.

Hi jSO. Typical shop compressors are either reciprocating piston (smaller ones) or screw compressors (larger machines). There are a handful of other types, but for the most part they are all "positive displacement" type machines. The flow rate they put out is roughly constant throughout the range of pressure. If they put out 25 CFM at 175 psi, they'll put out only slightly more than that at 90 psi.

The main reason they don't put out exactly the same amount is because there is a 'void volume' in most positive displacement machines which allows some small amount of the gas to re-expand as for example the piston goes through a suction stroke. That re-expanded gas takes up more space if it starts off at a higher pressure and that expanded gas prevents a new batch of air from completely filling the compression chamber.

Other reasons for a loss of flow include valve and seal leakage. But for the most part, the losses are not large. Between 10 psi discharge and 150 psi discharge for example, most positive displacement machines will only loose 10 - 20% of the total flow depending on design.

I would like to expand Q_Goest's comment a bit. When you speak of PD devices, either mass flowrate or volume flowrate at standard conditions (i.e scfm) remains constant irrespective of discharge pressure, keeping suction pressure constant, but actual volumetric flowrate (i.e acfm) changes.

The calculation from scfm to acfm and vice-a-versa is
ACFM = SCFM*[(Pstd - (Pvpstd*RHstd))/(P1-(P1*RH1))]*(T1/Tstd)

Standard conditions are Pstd = 14.696 psia, Tstd = 60deg.F and RHstd = 0%
P1, T1 and RH1 are pressurised air parameters.

Generally, for small flowrates, the term P*RH can be neglected and the simplified formula will be ACFM = SCFM*(Pstd/P1)*(T1/Tstd)

If the air temperature is same before and after compression (you can consider the temperature after aftercooler) then the equation is much simplified to ACFM = SCFM*(Pstd/P1)

Likewise, CFM1/CFM2 = (P2/P1)*(T1/T2)

All these terms are in absolute units. If your examples says the flowrate at 175psig is 25 acfm then at 90psig, it is 25*(175+14.696/90+14.696) = 45.3 cfm (at actual conditions)

This method can be applied where you are reducing pressure by a pressure reducing valve after the air is compressed to 175psig at the compressor. If the compressor setting is changed to 90psig, rather, then adiabatic conditions are to be used for volumetric calculations.

Thank you! You guys are great.

This is exactly what I was referring to - the acfm vs scfm. I was becoming very confused because it seems that some retailers are listing acfm, some scfm. It's hard to know which one the manufacturer is using on their website, and then when you call a retailer for tech questions even they don't know exactly which one is being referred to or which one is more relevant...

I was looking at some specs similar to these, where the cfm changes a great deal with PSI:
http://www.aircompressorworks.com/chartskaeser.htm

But then I was calling and asking certain manufacturers for the numbers, and I was getting cfms that only increased by maybe 1 cfm for a drop in 90 psi...basically no change at all.

As a person just looking to get a compressor which will work for my tools, I just need to know which one is relevant - acfm or scfm? If I have a tool requiring 20 "cfm" @ 90, then does that likely mean acfm or scfm? Perhaps I really need to ask the maker of the tool to specify..

If you can help me with this I would greatly appreciate it. Also, the equation is exactly what I was looking for, knew it had to be pretty simple... Thank you!

quark said:
This method can be applied where you are reducing pressure by a pressure reducing valve after the air is compressed to 175psig at the compressor. If the compressor setting is changed to 90psig, rather, then adiabatic conditions are to be used for volumetric calculations.

Can you clarify this a bit for me?

1) Since the two pressures I'm always comparing are 175 and 90, can I simply use this:

listed cfm @ 175 * 1.81 = acfm @ 90
?

2) A powder spray gun I have requires exactly 90 psi, which is set by a gauge on the tool. Does this gauge qualify as a "pressure reducing valve" (and thus allow me to use the above formula)?

3) What does this mean exactly?

quark said:
If the compressor setting is changed to 90psig, rather, then adiabatic conditions are to be used for volumetric calculations.

Thank you.

johnnyShopOwner said:
1) Since the two pressures I'm always comparing are 175 and 90, can I simply use this:

listed cfm @ 175 * 1.81 = acfm @ 90
?

Yes, provided listed cfm is acfm at 175 psig

A powder spray gun I have requires exactly 90 psi, which is set by a gauge on the tool. Does this gauge qualify as a "pressure reducing valve" (and thus allow me to use the above formula)?

Yes.

What does this mean exactly?

The above equation I wrote considers isothermal condition i.e PV = constant. When you are decreasing the pressure in a pressure reducing valve, the temperature change in the fluid is not significant (at least for the sake of calculations). That is why, you can neglect the ratio of temperatures.

However, when you do the compression, the process is adiabatic and pressure volume relationship will be governed by PV^k = constant, or if you know the temperatures before and after compression, you can use universal gas law. i.e PV/T = constant. This makes the volumetric difference when you operate the compressor at various cut off pressures, like indicated in the link you mentioned.

As Q_Goest suggested, there will be more losses when you increase pressure. The flowrate mentioned in your link seems to be ACFM.

It is always better to ask the manufacturer at what condition he specifies his flowrates. Generally, they mention it as FAD (free air discharge) which is scfm.

Tool consumption is generally quoted in scfm. Secondly, 20 cfm is quite a lot of air and it can't be acfm.

Regards,

Hi jSO. I see you got lots of good advice from quark already. (PS: quark, thanks for the papers regarding friction factor. I'll have to get back to you some time on that.)

I was looking at some specs similar to these, where the cfm changes a great deal with PSI:
http://www.aircompressorworks.com/chartskaeser.htm

I'm somewhat familiar with Kaeser compressors, and I know they make screw machines among others. I suspect the models listed on the link are screw compressors which are positive displacement types. See also this link for a little more background in the difference between positive displacement and dynamic compressors:
http://www.plantservices.com/articles/2005/257.html

The fact that particular link has a roughly linear variation of flow with pressure might indicate they're talking about ACFM at the outlet, but that's rather unusual. Generally we talk about SCFM and from what I can glean from that page, I'd say they're referring to SCFM. Here's why:

You'll note that in the above link I provided they talk about methods to vary compressor discharge.
Slide valve control is unique to rotary screw compressors. The slide valve varies compressor displacement by returning air back to the suction. Some slide valve applications also vary the discharge port location, which varies the volume ratio. Lift valve unloaders also allow air to return to the suction. The fixed location of the lift valves results in stepped capacity control as opposed to a slide valve’s stepless control.
A sliding valve control doesn't actually route compressed gas from the discharge back to the suction, it actually reduces the amount of air being compressed by changing the amount of gas picked up by the screws. Without as much air to compress, it can use the same power motor to compress a smaller amount of gas to a higher pressure or conversely a larger amount of gas to a lower pressure. This is controlled automatically by the PLC in the machine. Most screw machines have this feature built in.

The advantage of this arrangement is that it allows the machine's motor to put out a constant power over the entire range of pressure the compressor is capable of discharging to. By using all the power available, you can get more flow at lower pressure instead of having to size the motor for the highest pressure only. If it were a constant displacement over the entire range, then your motor wouldn't work very hard at low pressure, and would work harder and harder as discharge pressure increased. So the advantage of using the slide valve in a rotary screw is that it allows the machine to compress a larger volume of gas at low discharge pressure than it would otherwise be able to compress.

I did a few calcs to verify the power output given in your link and it came out exactly as if they had this sliding valve so I think there's little doubt the Kaeser machines are using this sliding valve and that's why they list the variation in flow depending on discharge pressure.

Note that there's also quite a bit of energy savings using this arrangement. The cost of electricity will be less for a machine that uses some kind of variable flow device like this.

If you're running some machine that needs 20 SCFM at 90 psi, the most cost effective solution is to run your compressor at just above that level. From the link you gave, the SX6 with 5 hp is capable of 23 SCFM at 100 psig which is your best solution for this demand. It can keep up with your demand of 20 SCFM at 90 psi, but it can also then continue to compress at a slower rate all the way up to 190 psi.

If you have enough money for a screw machine, they're probably your best option for this duty. They don't have wearing parts like a recip or other machines (ie: rotary vane) so they easily outlast those other types. And the cost of electricity if you use this machine daily will generally exceed the cost of the machine fairly quickly, so you should consider the cost of power when selecting a compressor.

Great posts guys. If there was one thing I would wish people to take from your info is the imprtance of rating on SCFM.

JSO said:
This is exactly what I was referring to - the acfm vs scfm. I was becoming very confused because it seems that some retailers are listing acfm, some scfm. It's hard to know which one the manufacturer is using on their website, and then when you call a retailer for tech questions even they don't know exactly which one is being referred to or which one is more relevant...
Good eye. You definitely have to pry that information from suppliers. Making the assumption one way or another can lead to trouble. A lot of times, I try to get through the front line phone answerers and get to an engineering salesperson for the supplier. They usually have no issues with getting you information.

Q,
I was always under the impression that screw machines had a higher maintenance requirement. Perhaps that is only for oil free machines and not a flooded screw?

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Hi Fred.
I was always under the impression that screw machines had a higher maintenance requirement. Perhaps that is only for oil free machines and not a flooded screw?
Interesting. Our company uses a lot of machines, and when we can we'll use screws over recips. I've heard that when dry screw machines first came out they were rather finiky and would often break down prematurely, but since then even the dry machines have become quite reliable. Still, the oil flooded screws are considered the most reliable. Recips work great in a garage or in installations where it's only running part time, but if you're looking for a process machine that's running 24/7 we've always used the oil flooded screws.

thanks for the great info!

So, what I'm gathering is:

1) scfm doesn't change (much) with psi on a recip compressor, but it DOES on a screw type compressor

(you are correct that the kaeser link points to rotary screw compressors)

2) acfm does change a good bit with psi. but that must not always be the case! as I found this link pointing to recip compressors:

http://www.aircompressorworks.com/chartscurtis.htm

*** You'll notice how the acfm is changing a good deal with psi on the SINGLE-stage but it's hardly changing at all with the TWO-stage compressors.

This is something else I really noticed when shopping.

Why does it seem that single stage compressors actually DO have a big change in acfm with psi, but two stage compressors do not?

Hi jSO. This might get a bit confusing. The use of the term "ACFM" can have slightly different meanings depending on context. Quark gave you the conventional description, and what he gave you is correct. Unfortunately, that's not the way the link you referenced is using it. They're using the term slightly differently. I'm referring to the link here:
http://www.aircompressorworks.com/chartscurtis.htm

In this case, compressor manufacturers will try and 'cover their ass' by telling you what the compressor displacement is instead of how many SCFM it will produce. They do this because conditions may vary depending on ambient pressure and temperature. I guess I can't blame them, but I agree with your OP that it does make it confusing.

What they are giving in that link you mentioned - is the actual displacement of the cylinder/piston at the given RPM. I can check this very easily by calculating horsepower versus pressure and flow, so I can be sure what they are trying to convey in this chart. The link (Challenger Air Compressors) is giving you the displacement of their machine, very much analogous to the displacement of a car engine, say a 426 cubic inch Hemi for example. The 426 is the engine displacement (specifically stroke length times area for all 8 cylinders). For the case of the Challenger air compressor, it's giving you the displacement also. It's not calculated exactly the same way as the Hemi, but the idea is very similar.

If you live in Denver during the summer where ambient pressure is 12 psia and the sweltering temperature of 105 degrees F, the density of the air going into the machine is lower than it would be at sea level on a 70 degree day. To determine SCFM from the charts given by Challenger, use the calculation provided by quark above. Note that all pressures are absolute and all temperatures are also absolute. To find absolute temperature, add 460 to the degrees F, so 70 F = 530 Absolute (also called Rankin).

For example, model O5HS3 provides 2.0 ACFM at 100 psig. In Denver, at 12 psia and 105 F, the SCFM produced by this machine is:

SCFM = 2.0 * (12/14.7) * ((460 + 70) / (460 + 105)

SCFM = 1.74 SCFM

As you can see, it's not much lower than the ACFM. If you live below Denver and you have the machine where temperature is roughly 70 (+/- 40 F), I wouldn't worry about trying to convert all this. It's not necessary. You're looking for a compressor in the 20 CFM range. You're not worried if it's 19.5 CFM or 20.4 CFM.

Hopefully that clears up any confusion around the link you pointed to.

1) scfm doesn't change (much) with psi on a recip compressor, but it DOES on a screw type compressor.
Note that both machines are positive displacement types. The only reason the Kaiser screw machine produced a variable flow is because of a special valve incorporated into the machine. I don't suppose that matters too much to you, but I thought I'd point it out being the nit picker I can sometimes be.

Why does it seem that single stage compressors actually DO have a big change in acfm with psi, but two stage compressors do not?
short answer: the individual states have smaller compression ratios so the gas that I mentioned earlier (in the void volume) that re-expands, is much less for a 2 stage machine. There are other factors including the leakage issue I mentioned, as well as a heat transfer/thermodynamic issue. When gas is compressed it gets hot, and that heat warms up the cylinder. The warm cylinder heats the incoming gas. The warmer the cylinder, the warmer the incoming gas was. Remember the ACFM stuff? The temperature is affected. Instead of 105 F for Denver, the gas gets heated before it can be compressed because the cylinder is already hot. The higher the compression ratio, the hotter the cylinder, and the warmer the gas will be before being compressed. Ok, that was as short as I could make it.

~

Side note 1: I mentioned you should consider the screw compressor over the recip. Maybe that's just a predisposition I have. I'll take back that recommendation. It really depends on economics, doesn't it? If you only use the machine a few hours a day, a recip may do just fine, and cost a whole lot less to boot.

~

Side note 2: We talk about SCFM having a specific pressure and temperature just as quark had mentioned. Unfortunately, you will find that industry standards use different values for pressure and temperature, and different parts of the world will also. For example, I work for an industrial gas company, and they use 14.7 and 70 F as standard conditions. I believe the petroleum industry uses a different standard. In Europe, they use "normal meter cubed" instead, and the temperature they use is often around 0 C as I recall. If you buy or sell gas, you may want to ask your supplier what values they use, as they may not coincide with the academic values.

Q_Goest said:
Hi Fred.

Interesting. Our company uses a lot of machines, and when we can we'll use screws over recips. I've heard that when dry screw machines first came out they were rather finiky and would often break down prematurely, but since then even the dry machines have become quite reliable. Still, the oil flooded screws are considered the most reliable. Recips work great in a garage or in installations where it's only running part time, but if you're looking for a process machine that's running 24/7 we've always used the oil flooded screws.
I defintely don't use them that much. When I do, it is in large volume requirements (the last time was about 55 SCFS). Just in discussions with the manufacturers, it was commented that the dry screw machines usually needed some kind of overhaul in approximately 2500 hours versus a flooded screw. We have two flooded machines that have been around for years and have never had a major overhaul except for the fuel controls.

I was asking more out of personal curiosity than experience. The compressors I deal with the most are axial compressors at the front of engines.

quark said:
Tool consumption is generally quoted in scfm. Secondly, 20 cfm is quite a lot of air and it can't be acfm.

Yes, I checked with the tool manufacturer and they say it needs 20 scfm @ 90.

I also found this website, which seems pretty helpful (despite all the ads..):

http://www.engineeringtoolbox.com/scfm-acfm-icfm-d_1012.html

## What is the formula for calculating cubic feet per minute (CFM)?

The formula for calculating CFM is: CFM = (Volumetric flow rate, in cubic feet) / (Time, in minutes).

## How do you convert CFM to PSI?

To convert CFM to PSI, you will need to know the specific gravity of the gas being measured. The formula for this conversion is: PSI = (CFM x Specific Gravity) / 7.48.

## What is the difference between CFM and PSI?

CFM stands for cubic feet per minute and is a measure of volumetric flow rate, while PSI stands for pounds per square inch and is a measure of pressure. CFM measures how much air is moving through a system, while PSI measures the force of that air on a specific area.

## How do you measure CFM and PSI?

CFM can be measured using a flow meter or a pitot tube, while PSI can be measured using a pressure gauge. Both measurements require specific instruments and techniques to ensure accuracy.

## What factors can affect the accuracy of CFM and PSI calculations?

The accuracy of CFM and PSI calculations can be affected by factors such as changes in temperature, humidity, altitude, and the type of gas being measured. It is important to consider and account for these factors when performing calculations to ensure accuracy.