How Long Will It Take for a Balloon's Pressure to Equalize Through a Small Hole?

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SUMMARY

The discussion centers on calculating the time it takes for a balloon's internal pressure of 9.7 KPa to equalize with ambient pressure through a small hole of 0.25 mm². The user initially considered simplifying the problem by modeling the balloon as a hollow cylinder and calculated the force exerted by the air at 2.425 N, with an air expulsion speed of 127 m/s. The user sought confirmation on these calculations and inquired about the applicability of Bernoulli's equation, ultimately resolving the problem independently.

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Homework Statement



I have a balloon full of air, it is at a pressure relative to the ambient pressure of 9.7KPa and its volume is 3000cm3. The balloon is attached to a surface, this seal is airtight and perfect. The surface it is attached to contains a (very) small hole with an area of 0.25mm2. I am struggling to figure out how long it will take for the pressure within the balloon to equal that of the ambient pressure within the room.

Homework Equations



This is what I am stuck on, I don't have a clue which equation to use.

The Attempt at a Solution



I thought that I would start at simplifying almost everything, instead of imagining a balloon attached to a surface I could just imagine a hollow cylinder with a volume of 3000cm2 and the same pressure being synthesised by a force acting on top of the air seeing as though the pressure within the balloon doesn't change until the very last second which I can neglect. I though about imagining it like a syringe with a constant force.
I calculated that the force of the air after being forced through the hole will be 2.425N. I think that is right, I also figured out that the air would be expelled at 127m/s but this seems a little high, can someone confirm this?

I would very much like this to be almost totally my own work so if you could just give me a few gentle nudges or a couple a links to a web page I would be eternally grateful.
 
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Can I use Bernoulli's equation? Or is that fluids only?
 
Never mind, solved it myself
 

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