# Fill time for a pressurised system

1. May 30, 2012

### sph99

Hi everyone

I have a problem whereby I need to calculate the time to fill and then deflate a catheter balloon. This consists of a hand pump connected to a long tube which then widens out to the balloon vessel. I need to reach a certain pressure in the balloon. The balloon is already expanded and it is assumed no further expansion of the material will occur.

I know the volumetric flow rate (Q) from the hand pump. The length (L) of the tube is 1400mm. I have calculated the pressure drop across the tube (delP).

How to I determine how long it will take to fill both the tube and the balloon from vacuum to a given pressure and then how long to pull a vacuum on the system? Any help appreciated.

I previously used Pressure = mass*Gas Constant*Temperature/Volume. I did this at intervals until the pressure in the vessel equaled the pressure required, giving me the time required. However I found that this did not match my experiment. (The calculated times were much greater than the actual)

(I posted this earlier in the wrong the wrong forum, sorry)

2. May 30, 2012

### Q_Goest

Hi sph99, welcome to the board.
It should be as easy as determining the mass needed to fill the volume of the catheter and tube (you can assume ideal gas), then divide by the mass flow rate of the hand pump to get time to fill. Note that the gas required to fill the catheter and tube is the final mass of the gas less the initial mass of the gas. If this calculation doesn't mirror the actual experiment, check your assumptions for volumes, pressure, etc...

I would neglect any pressure drop through the tube for this since the time it takes for gas to travel the length of the 1400 mm tube is going to be negligible.

3. May 31, 2012

### sph99

Q_Goest, thanks for your reply. I should have pointed out that this balloon is filled using water or saline and not air. Am I correct in saying that I cannot then use the ideal gas laws?

I have looked at Bernoulli but I dont know how to apply this when one end of the system is closed. Also it does not take into account the viscosity of the fluid.

Last edited: May 31, 2012
4. May 31, 2012

### Q_Goest

Ok, if it's filled with a liquid, the ideal gas equation doesn't apply. Just take your two volumes and calculate the mass needed. The only thing you need is the liquid's density. You said you already have the pump flow rate so you don't need to analyze pressure drop or anything else, so there's no need for Bernoulli either.

5. May 31, 2012

### sph99

that will only work for atmospheric pressure. I want to determine the time to reach a higher pressure (600kPa). how do I find mass at a certain pressure?

Last edited: May 31, 2012
6. May 31, 2012

### Travis_King

You are trying to pressurize a catheter to 90 psi?

7. May 31, 2012

### sph99

Yes, 6 atm or 90 psi is a fairly standard inflation pressure for coronary catheter balloons.

8. May 31, 2012

### Q_Goest

Does the catheter stretch at 600kPa? I suspect it does. I wouldn't worry about a difference in saline density. That's not going to be measurable. But I suspect the catheter stretches, in which case it would be easiest to measure the increase in volume.

9. May 31, 2012

### sph99

No, the balloon is moulded into shape before use and will not stretch at 600 kPa

10. May 31, 2012

### Q_Goest

So you know the volume of the catheter and tube at 600 kPa then?

Is there anything else you're confused about?

11. May 31, 2012

### sph99

Thanks!

I also need to work out deflation time but that's just the same thing in reverse.

I have to also work out the inflation time at 1800kPa. The balloon will stretch in this case. How would I go about that? It is a safety check that we must do.

Thanks again

12. May 31, 2012

### Q_Goest

That's basically the same calculation. You'll need the final volume so you can determine the mass of saline solution in the catheter and tube at 1800 kPa. It could be very difficult to determine the final volume analytically. I'd suggest doing a test on it.

13. Jun 5, 2012

### sph99

Thanks Q_Goest, but my calculations are not agreeing with my experiments. The calcs are give me less than a second, the experiment giving me 5 seconds. I am happy that the flow rate is accurate. I think this is due to the long length of very small diameter tube. The length of the tube is 160mm but its diameter is less than 1mm.
Have you any idea what I need to introduce to my calculations to allow for this?