Volumetric flow rate conversions

[Daniel Sellers]

I'm trying to learn more about how air compressors work (not how they mechanically function - how they're input/out pressures and flow rates work) and I'm having a lot of trouble getting a specific questioned answered even after a lot of google searching.

Suppose I have a compressor that the manufacturer states has a flow rate 1.35 CFM and a maximum pressure of 150 PSI (please feel free to post answers using any units, I'm not attached to the obnoxious US ones). If I'm using this compressor to fill a known volume with air of a specific pressure, how do I calculate how long it will take to fill the volume? Let's say the volume can be regulated for temperature, or that entire process is isothermal.

Different sites and documents available describe different specs and calculations for air compressors but so far none of them have been much help in answering this question.

 

[Daniel Sellers]

For instance, this site has a calculator available which does exactly what I'm trying to figure out. If anyone could tell me what equation this calculator is using, it would be greatly appreciated.

http://www.egnergy.com/calculator.html

 

[anorlunda]

Just a guess, the perfect gas law, PV=nRT.

If you don't know what that is, look it up on Wikipedia.

 

[Daniel Sellers]

Just a guess, the perfect gas law, PV=nRT.

If you don't know what that is, look it up on Wikipedia.

I definitely know the ideal gas law. What I don't know is how the flow rate at the inlet pressure is converted to a flow rate at the pressurized volume. Are you suggesting I use the ideal gas to convert the volumetric flow rate to a mass flow rate and then calculate what volume that mass would occupy at the target pressure? Cause now that I took the time to write that all out it sounds like a good idea?

 

[anorlunda]

Basically yes.

 

[Daniel Sellers]

I definitely know the ideal gas law. What I don't know is how the flow rate at the inlet pressure is converted to a flow rate at the pressurized volume. Are you suggesting I use the ideal gas to convert the volumetric flow rate to a mass flow rate and then calculate what volume that mass would occupy at the target pressure? Cause now that I took the time to write that all out it sounds like a good idea?

Basically yes.

Alright so I did that, and I'm getting fill times which are similar to that calculator with about 10% discrepancy.

I solved the ideal gas law for mass in order to convert a volumetric flow rate into a mass flow rate, then used that mass flow rate to calculate the volumetric rate at target pressure. The only thing I didn't account for is potential temperature change.

But while typing this I realized I can use a combination of Charles' law and Boyle's law to calculate the amount the temperature would change and plug that into equation. @anorlunda you genius!

 

[Daniel Sellers]

Nope nevermind, that does not work. One equation assumes constant temperature and the other constant pressure. So can anyone explain how to account for temperature change in the process I've out lined above? Should I just assume the process is isothermal?

 

[Nidum]

The total time to fill the volume with air is something which you can set using the outlet valve from the compressor .

Whatever the chosen setting of the outlet valve the filling of the volume is not going to be at a constant rate .

The pressure difference between the compressor tank and the volume goes from a higher value to a lower value as the volume is being filled .

Flow rate depends on pressure difference and effective flow area .

If as seems likely the required pressure in the volume being filled is quite low compared to the available pressure from the compressor and if the volume only needs to be filled relatively slowly then a very simple model of this filling system can be used .

You can reasonably assume that the compressor is a constant pressure source .

Effective flow area is probably going to be the area of opening of the compressor valve .

Over to you now :

Do you think that any significant changes of air temperature are likely to occur during filling ?

Can you sketch a system diagram ?

 

[Daniel Sellers]

The total time to fill the volume with air is something which you can set using the outlet valve from the compressor .

Whatever the chosen setting of the outlet valve the filling of the volume is not going to be at a constant rate .

The pressure difference between the compressor tank and the volume goes from a higher value to a lower value as the volume is being filled .

Flow rate depends on pressure difference and effective flow area .

I figured the pressure difference and throughput of the compressor will affect fill time, my question is in what way? What might I search to learn more about how, specifically, flow into the pressurized volume depends on these or other quantities involved?

If the compression is slow and the system is not well insulated then perhaps there will not be a significant temperature change. According to the ideal gas law, temperature will be proportional to the product of pressure and volume.

But why do we have to assume that the volume pressure is much lower than the compressor's output? Just because it would become terribly inefficient otherwise?