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

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The discussion revolves around calculating the time it takes for the pressure in a balloon to equalize with ambient pressure through a small hole. The balloon has a pressure of 9.7 KPa and a volume of 3000 cm³, with a hole area of 0.25 mm². The user initially considered simplifying the problem by visualizing the balloon as a hollow cylinder and calculated the force of the air being expelled at 2.425 N, estimating an air expulsion speed of 127 m/s. The user sought guidance on whether to use Bernoulli's equation for this scenario but ultimately resolved the problem independently. The thread highlights the challenges of applying fluid dynamics principles to real-world scenarios.
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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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
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