In reality, I imagine the chambers would all simply flood.
However, on paper It seems that Chamber 1 would flood, Then as it hit 999 pounds of pressure (When Chamber one is almost entirely flooded) the second chamber would begin leaking and the air in chamber 2 would begin leaving to chamber 1, whereby most of it would leave through the hole but a small amount would remain trapped. When chamber 2 fills to 999 pounds (which would take much longer than it took chamber 1 to fill) , Chamber 3's air would have to start leaving, but since it would have to pass through Chambers 1 and 2, both of which in theory are 99.99% flooded, It would take some deal of time for this to happen.
Basically, each chamber would fill progressively slower, but would always retain some small amount of air in the upper corners. In theory the air pressure in Chamber 3 (or some subsequent chamber) might very well equal enough to prevent the water from chamber 2 from entering.
If I might suggest, someone with a larger bathtub than myself should try building a model of this. It would be very interesting to see the results.
|