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Secret agent Bond is escaping from a submarine through its tower. Initially the pressure in the tower is the same as the air pressure on the water: p0=\SI100kPa. After closing the hatch that separates the tower from the rest of the submarine Bond makes a hole inside the tower’s wall (see figure), after which the tower partly fills with water. Next, Bond opens the ceiling hatch and swims to the surface with the released air.
a) How thick is the air layer that is inside the tower before opening the ceiling hatch and after the water has stopped flowing inside?
b) How big and to what direction (up or down) is the total force applied to the ceiling hatch by the air and the water before opening the hatch and during the time when the water level inside tower has stilled?
The area of the hatch is $S =
\SI{0,50}{m^2},thewaterlevelabovethehatchh=\SI{25}{m},theheightofthetowers=\SI{2,0}{m}.Thedensityofwater\rho = \SI{1000}{kg/m^3},gravitationalaccelerationg =
\SI{9,8}{m/s^2}$.