How does air compress?

I have a tube with air trapped b/w water (air compressibility is ignored). This tube is connecting 2 reservoirs. In one of them the level of the water is being increased and in the second one the end of the tube is submerged 0.2m below the water in the tank. They are asking me to find when will air bubbles start appearing in the second one. I found it. Now they want me to account for compressibility. How do I do that?