# 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?

• The forces need to balance, and force is pressure*area. So the difference in pipe diameters and overflow areas (shower basin vs toilet bowl) must result in a balance of the force on the water. I'll let somebody work out a more full answer, currently studying! Oct 16, 2013 at 22:18
• @tpg2114 How does that differ from something like this? In that case the openings to the air are different diameters, should receive different forces from pressure, but remain at equal depth. Oct 16, 2013 at 22:23
• Yeah, tpg2114's answer probably isn't right. The water level should be the same at equilibrium. Or at least, it should be the same if the simple picture of them being tubes with open ends is correct. For the shower basin, this is probably true, but for the toilet, I'm not so sure (toilets have a raised water reservoir, and I'm not sure if this is connected with the bowl supply which supplies a pressure). Perhaps this would be more fit to ask at PlumbersExchange? Oct 17, 2013 at 2:31
• @DumpsterDoofus Here's a diagram of a toilet. The tank isn't connected to the system in a meaningful way, although there could certainly be some bit of plumbing that matters further down. The toilet pipe DOES twist around a bit (it's usually a siphon), would that matter when the water level is above the "hump" in the pipe? Oct 17, 2013 at 2:38

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.