If I understood correctly you are referring to an equivalent situation to submerging a glass in a tank of water, inverting the glass upside down, and lifting the bottom of the glass above water level? Except in this case you want to evacuate the air after the fact?
If those presumptions are correct the total force needed is simply equivalent to the weight of the water lifted above the water level of the lower tank 1/2 the maximum height of the second tank, presuming the circumference of the upper tank is constant at all heights. Depending on your purpose there is likely other issues I can only guess. If the psi exceeds atmospheric pressure it also causes problems, but this has more to do with the surface area, or total height of the upper tank, than it does total volume of water.