Sounds more like a physics project to me.
Anyway, take a rubber stopper with two holes; one is large, the other smallish. To the large one, attach a semi-flexible hose, something that will make a good seal, but not get crushed or pushed out easily. It has to be able to bend into the opening of the other bottle. Now, take that large hose and fit it so that it fits to the bottom of the 2L bottle with the water.
For the smaller hole, make it out of some sort of tubing that can withstand a reasonable amount of pressure, but is still reasonably flexible and can make a good seal. It doesn't have to go far into the bottle at all. Attach one end to a tank of pressurised gas. Turn on the pressure. You'll blast the water out of that container. You'll need to work on the pressure settings to get it right, but it can be transferred very fast. This is the principle of using a canula in air-sensitive chemistry (Schlenk technique). It's used all the time with glass vessels, needles, etc. In your case, if you make the diameter of the hose big enough, you should be able to dump the contents of one container into the other very rapidly.
The problem with this is that you may not have access to compressed air or the like. Check your fume hoods and see if they have a compressed air or nitrogen outlet. Those are your best bet. Gas jets, in addition to emitting flammable gasses, are absolutely useless because their pressure is incredibly low.
Be careful not to over pressurize the plastic bottle, too. You start using cylinder gasses and you can blow a bottle up with no problem pretty quick.