GeekDad Puzzle of the Week: Another Great Escape

Your Thanksgiving plans are interrupted by evildoers and their schemes. It being Thanskgiving and all, mailto:wired.geekdad@gmail.com your solutions by 11:59 p.m. EST Thursday to be part of the random selection of correct answers and win a $50 gift code to ThinkGeek!
All readers who check out the solution on Friday will receive a gift code for $10 off of their next ThinkGeek purchase of $30 or more. Puzzle after the jump.

Special thanks to ThinkGeek for providing our prizes!

It's not easy being a genius. All sorts of nefarious characters think they can just have use of your brilliance for whatever evil scheme crosses their mind. So it was that you found yourself abducted in the wee hours of the morning and held captive in the evil but very bizarre lair of some character who calls himself Frunobulax.

Blah, blah, he wants you to build a time portal so his henchmen can go anywhere and work their evil deeds, blah, blah, your life is on the line…the usual. And this being the week of Thanksgiving! Luckily you've escaped and are making a hasty exit through some sort of utility access-way. Your way is suddenly blocked except for a single perfectly cylindrical tunnel that extends through an empty sphere end-to-end. The sphere is suspended in a vertical conduit with other spheres like it above and below.

The warning pictograms on the wall indicate that to pass through the tunnel, the sphere must be filled with liquid or else it will not support your weight and come crashing down in the seemingly endless drop. The flow of liquid is controlled by a panel on the wall. More warnings reveal that if too much liquid is released, the sphere will come crashing down. If too little, your weight will bring it down as you cross through. The only way to traverse the tunnel is to release the perfect volume of liquid via the panel to fill the sphere. One pictogram shows the length of the tunnel from opening to opening to be 20 meters. Another shows that only one panel input per side of the tunnel is allowed before the panel locks for safety reasons. You hear voices and footsteps and must move fast if you are to escape.

What volume of liquid do you punch in to fill the sphere?