Quoted: say you have a 4’ tall 50 gal tank full of water. it' can be sealed and can be pressurized. it also has a drain line on the bottom and the drain runs back up alongside the tank to the top. So the drain vent is 4’ tall. You vent it to atmos and fill the tank with water and the drain line fills. (simple) The pressure at the base of the tank is about 2 PSI and 50 gal also holds 6.6 standard cubic feet.
Let’s say you attach an air cylinder to the vent on the top of the tank and begin applying pressure. The drain is open. As you apply more and more pressure water begins flowing out the drain. First of all how many standard cubic feet of air must you have in the cylinder and what pressure must it be at to completely evacuate the tank?
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Well, I'm not going to crunch the numbers, but you would need enough pressure to lift the entire 50 gallons 4 feet off the ground (in order to get it out through the vent). So, the weight of the water divided by the surface area in the tank will give you the pressure.
If you know the pressure in the tank once it is completely evacuated, then you can calculate the amount of gas you need.
The problem is that as the tank empties, you'll need less and less pressure (less water to lift). That throws the calculations off if you want to remain economical. You'd need to do some calculus.
That's what occurs to me off-hand. Hope it helps.