Get Out!
by Peter Jägare
You can't flood the room, because the marbles are just precisely too small...
Well, what if you can make them larger? This is actually not particularly complicated, due to the physical principle that says that substances expand as they get hotter (this is what makes standard mercury or ethanol thermometers work, and also why you can run hot water over the lid of a jar to make it easier to remove). There's a source of heat available - the water in the urinal. The door, being wooden, will swell and make a tight seal with the doorframe, and all you have to do is paddle water until you can reach the window.
Which admittedly might take a while. But, it's a pretty small room, and the water is flowing quickly, so you'll probably make it.