# Average gas flow of a syringe

InterestingStuff
Hi, I tried looking for similar topics but nothing really solved my problem.

How can I calculate the average gas flow on a syringe that was compressed over time, if the starting and ending pressure and volume are known?

I am guessing there must be an equation which can relate these variables. So for instance if I started at 50mL, with a pressure of 5bar and after 10 minutes the syringe was at 40mL with a pressure of 10bar, what was the average gas flow? Thanks in advance.

Mentor
Are you familiar with the ideal gas law?

Homework Helper
Hi, I tried looking for similar topics but nothing really solved my problem.

How can I calculate the average gas flow on a syringe that was compressed over time, if the starting and ending pressure and volume are known?

I am guessing there must be an equation which can relate these variables. So for instance if I started at 50mL, with a pressure of 5bar and after 10 minutes the syringe was at 40mL with a pressure of 10bar, what was the average gas flow? Thanks in advance.
The first step is to figure out what sort of result you want.

Are you after a volumetric flow rate? How much volume over so much time? But that would not make much sense. You have a wide variation of pressure. At a high pressure, you lose a lot of gas without much volume flowing. At a lower pressure you can lose more gas with the same volume flowing.

At what pressure should you be assessing the flow rate? Maybe you want a volumetric flow rate based on the volume that the fluid would have at 1 bar and standard temperature.

Tell us what you want out of the calculation.

Gold Member
I believe you are going to need to define how the pressure ##P## changes in time.

This would not be the typical input for compressing gas in a syringe. What would typically be controlled in this type of scenario would be the change in volume of the gas per unit time ## \frac{d V\llap{-}}{dt}## (the very thing you seem to be after). Imagine markings on the syringe, we typically ask "if I'm controlling the rate at which the plunger passes a marking (units of volume), then how does the pressure in the syringe respond as a function of time".

Otherwise, the volumetric flow rate is whatever you want it to be. It's not going to be uniquely defined between initial and final states of volume and pressure.

EDIT:
Are we even ok to use the term volumetric flow rate in this instance? When I think of volumetric flow rate, I think of how much volume passes an arbitrary boundary intersecting the flow per unit time. If you imagine doing that at some arbitrary location in the "capped syringe" described, you can find a point (the cap boundary) where the "volumetric flowrate" is zero over the duration of the compression.

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Homework Helper
Are we even ok to use the term volumetric flow rate in this instance?
This appears to be a leaky syringe. So I was assuming "volumetric flow rate past the seal".

Gold Member
This appears to be a leaky syringe. So I was assuming "volumetric flow rate past the seal".
How do we know that?

jbriggs444
Homework Helper
How do we know that?
Starting pressure times starting volume is not equal to pressure times final volume. It's a ratio of 250 to 400. Which suggests either a large change in absolute temperature. Or... addition of gas. Whoops, that's not leaking out, that's leaking in at the same time someone is pushing on the plunger.

Are the numbers in this situation just made up from whole cloth?

Gold Member
Starting pressure times starting volume is not equal to pressure times final volume. It's a ratio of 250 to 400. Which suggests either a large change in absolute temperature. Or... addition of gas. Whoops, that's not leaking out, that's leaking in at the same time someone is pushing on the plunger.
Yeah, I believe that if the temperature is changing, we can't assume an isothermal process and ##P_1 {V\llap{-}}_1 \neq P_2 {V\llap{-}}_2 ##, and if we are adding gas to the syringe the mass is not constant and again and it shouldn't be valid to do that computation.

I think the part about them pushing on the plunger and gas coming "in" (passing the seal) is ok if the gas in the syringe is initially under relative vacuum to it surroundings.

Are the numbers in this situation just made up from whole cloth?
I would suspect they were just naively constructed numerical examples.

jbriggs444
Gold Member
However, those numbers don't appear to be out of the realm of possibility:

For a gas undergoing a process where the temperature isn't constant (but mass is fixed), we have that:

$$\frac{P_1 {V \llap{-}}_1}{ P_2 {V \llap{-} }_2} = \frac{T_1}{T_2}$$

For the numbers given this implies

$$\frac{T_1}{T_2} < 1$$

Heat must be added during the process. Which I realize now this is what you were implying.

Mentor
This thread seems to be a "hit and run" - the OP came back, took a look. No interaction. Probably got his answer elsewhere.

So, we'll lock the thread in another day or so.