Pumping water versus expulsion

[bgizzle]

Does it take the same amount of energy to lift water out of a tank as it would to force it out using compressed air? For example if there is a cylindrical tank that is 14 meters tall, 10 meters wide and it is filled with water to a depth of 5 meters I know that it takes 44.3e6 joules to lift that water out of the tank. (9800 n/m^3, 25pi, dy, 14-5... solved using integrals) Is there a formula for how much compressed air it would take to force the water out a vent on the bottom of the tank, assuming the tank is surrounded by water (but attached to the bottom so it wouldn't start floating as you pump in compressed air)?

My thought was it would take less energy to force water out because distance traveled would be less. So if say your tank is 1000 feet down and you wanted to pump the water up and out through a pipe or force it out through a vent, the compressed air way might take less energy. How much force of resistance are you meeting from the water outside the tank?

 

[mfb]

If the water ends at the same height and if we neglect all inefficiencies, it needs the same amount of energy. This is just energy conservation. In a real setup, that pressurized air will give significant losses.