I have a hemisphere dome, which volume = [itex]\frac{2}{3}[/itex]∏r

^{3}
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 cm

^{2} (2 x 10

^{-5} m

^{2}) 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