Water Level and Pipe Widths I ran into a bit of physics yesterday, and couldn't understand the physics at work. I've been scouring the Internet, but haven't found the answer yet. I'm guessing there's a basic principle I'm misinterpreting or ignorant of.
Basically, the sewer backed up into my house. Among other points of entry, water flowed up the shower drain, and up the toilet bowl.
The shower filled to a bit under the lip of its basin. The toilet filled to a bit under the lip of the bowl, but neither overflowed.
So basically I had a reservoir (the sewer), with one pipe (shower) extending to floor height + 4 inches, and another pipe (toilet) extending to floor height + 24 inches.
Where I'm getting confused is that in my physics textbooks I recall seeing a diagram of a U-shaped vessel with differently sized "legs." I think that the water level in each leg of the U had to be the same, because otherwise there'd be a pressure differential at the base of the U preventing the system from stabilizing.
Edit: Here's an example of what I'm talking about.
What would allow for this difference in water levels?
 A: To make a less apetizing point: The argument leading to the water levels being equal starts from an ideal fluid. Now a sewer backing up is far from ideal. I would expect solid pieces like toilet paper and feces clogging the pipe leading up to the shower (especially if the shower drain has a siphon), while the toilet drain is made for larger pieces fitting through.
A: What you're missing is some practical aspects of modern plumbing. Every modern plumbing fixture(toilet, shower/sink drain) has a trap or "u-bend" in the piping before it connects to the sewer branch or main pipe. This allows a pocket of water to sit in the bend of the pipe to keep sewer gases from escaping back into the room when the fixture is not being used. This water pocket obeys the equilibrium principle you know. When the fixture is used, the water above disturbs this balance and everything flows into the sewer pipe.
During your sewer back-up event, something has happened downstream to provide enough pressure reverse the normal flow, and the material will seek any free outlet (e.g. your shower drain). These events are usually very short-lived, so probably provided enough pressure to push stuff through the u-bend in the toilet and shower, then ceased. Once that pressure was gone, the normal physics applies and the liquid levels then reach equilibrium with their respective u-bends. Your shower basin, despite being lower than the toilet, contained the spill because it had a larger area to contain the volume of the spill.
Source: Plumbing design engineer.
More about plumbing traps here.
A: If you are concerned about the water height differences, then 
Every wash basin/toilet will have an over flow holes just around the lip of the toilet or just below the top surface of the wash basin. These tiny holes are not visible easily as it is made at places where it is not easily seen. This ensures the water level does not raise above certain level. That is why you not seeing overflowing.
As you mentioned that these 2 pipes are at different height, the water in these two actually wanted to maintain same height, they don’t. Because these overflow holes doesn’t allows them to rise without completely filling these pockets which are inside the basin/toilet itself. There will be a lot of space before it again reaches to main lines.  if you leave water for longer time, then you should be seeing it start filling these holes too and overflowing.
