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## Time taken for pressure to equalise?

I have a hemisphere dome, which volume = $\frac{2}{3}$∏r3
Inside the dome, pressure is 1atm (assume 1.05 kPa)
Outside the dome, pressure is 0.01atm (10.5 Pa)
I then puncture a 0.2 cm2 (2 x 10-5 m2) hole on the flat side of the dome.

Question: Find time taken for pressure to equalise.

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I have searched up the internet, and seems that I have to use bernoulli. But I have a few problems.

1) I have no idea what to substitute for the variables.
2) Are the density of air inside and outside the dome different?
3) How should I use calculus (or differential equations, or anything else) to find the time taken, given the process is non-linear in relation.

Thanks
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