# Calculating fill rate if pressure delta, volume, and time are known?

• wruehl1
In summary: I am not seeing the problem. If you are filling a vessel from a higher pressure to a lower pressure, the volume of the vessel will decrease as the pressure decreases. So the average flow rate will be lower. However, the instantaneous flow rate at any particular time may be very high. The regulation pressure will be higher than the ambient pressure, so the fill time will be shorter.
wruehl1
TL;DR Summary
If I know the starting pressure and ending pressure, volume of the vessel, and time to fill. Can I determine the fill rate or flow rate?
I am looking for an equation that I can use to compute L/min or mL/min for a 480cc vessel going from 150bar to 250bar with a fill time of 6min. Sensors for flow rate at these pressures are hard to find, but I thought there might be a way to work this out with the parameters known. An equation would be AWESOME if expressed in a way that I could automate via excel or sheets. Can it be done? Is anyone willing to look at this with me? I've tried searching this a bunch of different ways, I'll say it's challenging to find... It's also outside my wheelhouse. Thank you for time in advance.

Welcome!
How and with what fluid are you pressurizing that vessel?
The flow rate will be decreasing as the internal pressure increases.

You can determine the average rate pretty simply. That may (or may not) tell you very much about the instantaneous flow rate at any particular time - depends on the details of your 'filling apparatus.'

Lnewqban
wruehl1 said:
Summary: If I know the starting pressure and ending pressure, volume of the vessel, and time to fill. Can I determine the fill rate or flow rate?

to 250bar with a fill time of 6min
Are you actively cooling the pressure vessel while you fill it? If not, the final pressure will be lower after you stop filling it and it cools off...

That's one reason why scuba tanks are usually filled in a water bath (the other being explosion safety)...

Lnewqban
I am not, but the volume of the vessel and the low fill rate do not seem to elevate the temperature of the vessel much at all. I'm really just trying to come up with a "rough" fill rate to use as metric for compressor performance against a load.

Lnewqban and berkeman
Lnewqban said:
Welcome!
How and with what fluid are you pressurizing that vessel?
The flow rate will be decreasing as the internal pressure increases.
A 250 watt HPA compressor. Air is the media. Thank you for your inquiry!

berkeman said:
Are you actively cooling the pressure vessel while you fill it? If not, the final pressure will be lower after you stop filling it and it cools off...

That's one reason why scuba tanks are usually filled in a water bath (the other being explosion safety)...

View attachment 301839
I am with you 100%. I have 88CF bottles as well, and I agree that when you step up the fill rate, that contraction can be quite noticeable. The small vessel I'm talking about would be challenging to remove and fill, and the temperature delta with a 6 min fill is not large at all. Good advice to be sure, but not really much of a concern in this specific case. Just looking for a way to back calculate an average fill rate so I can compare compressor performance.

berkeman
Any simple air compressor is going to deliver less air as the outlet pressure increases. You will need that flow vs pressure information before you can do much more than compute average flows for specific situations. The compressor manufacturer almost certainly has that data (whether you can get it is another question). Given that data, what you want isn't too difficult. It would be a real science project to determine the compressor performance curve empirically (it can be done).
.

Lnewqban

The question I was trying to answer: An air compressor tank is regulated down to some pressure from its very large tank. This regulated pressure is used to fill a (rigid - fixed volume) tire. Will the fill time (where the pressure of the tire is the pressure at the regulator) of the tire be finite?

This is kind of a similar problem to what you are asking?

Maybe what I was trying will give you some direction.

I was imagining a control volume that was comprised of some hose, and a fill valve as forms of viscous dissipation.

Then I was trying to apply the CoE result commonly found in the study of fluid mechanics:

$$\dot Q - \dot W_s = \frac{d}{dt}\int_{cv} \left( \frac{V^2}{2} + gz + u \right) \rho \, dV\llap{-} + \int_{cs} \left( \frac{V^2}{2} + gz + h \right) \rho \, \boldsymbol V \cdot d \boldsymbol A$$

I think this is the relationship you are going to have to alppy to get started.

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I really think this is being complicated beyond what is needed. If I know the volume of the container (480cc) and the pressure I started at (150 bar) and it took me 6min to get to 250bar. What volume of gas (air in this case) would it take to create that difference in pressure? Divided by the time it took to get there? Assuming the rate is slow enough to not add excessive heat, which it is. I must be missing something... Like I said, not my wheelhouse.
I'm aware this is an aggregated value, rather than an instantaneous rate, and that's ok it's only meant to compare one cheap compressor against another.

erobz
I think you can say this:

Assumptions:

Constant fill tank pressure ( absolute ) attached to the compressor ## P_{c} = {P_c}_g + P_{atm} ##

Isothermal Expansion: ##T_c = T_{filled} ##

Constant tank (you are filling) volume ## V\llap{-} ##

Then the average volumetric flow rate leaving the compressor tank ## \dot{ {V\llap{-} }}_c## ;

$$\dot{ {V\llap{-} }}_c = \frac{ \Delta P}{ \Delta t } \frac{ V\llap{-}}{P_c}$$

Where ## \Delta P ## is the change in pressure of the tank being filled

EDIT:
Thinking about it, I don't see how that helps you compare compressors. Different compressors provide different flow rates (SCFM) at different pressures. What you should be comparing is the ratings from the manufacturer. You might instead examine net fluid power ( this measure factors in compressor efficiency) delivered vs flow if you are trying to compare them across manufacturers.

Last edited:

## 1. How do you calculate fill rate if pressure delta, volume, and time are known?

The formula for calculating fill rate is: Fill Rate = Volume / Time. However, if the pressure delta is also known, the formula becomes: Fill Rate = (Volume * Pressure Delta) / Time. This takes into account the change in pressure over time, which can affect the fill rate.

## 2. What is the unit of measurement for fill rate?

Fill rate is typically measured in units of volume per unit of time, such as liters per second or cubic feet per minute.

## 3. Can fill rate be affected by external factors?

Yes, there are several external factors that can affect fill rate, such as temperature, viscosity of the fluid being filled, and the size and shape of the container being filled.

## 4. How can pressure delta be calculated?

Pressure delta can be calculated by subtracting the initial pressure from the final pressure. This can be measured using a pressure gauge or by using pressure sensors.

## 5. Is there a maximum fill rate that can be achieved?

Yes, there is a maximum fill rate that can be achieved for a given set of conditions. This is often determined by the equipment being used and the properties of the fluid being filled, such as its viscosity and surface tension.

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