The Big Bang Theory, gives us not just toilet humor, but a contemporary physics controversy, too. Tonight Raj worries about how Aquaman uses his toilet. How can he flush it underwater?
The most common toilet in North America is a spectacle of physics, the “siphoning toilet”. Using a design honed for over two thousand years, here’s how the toilet works: Water sits in the bowl of the toilet just below the level of the top of an S-shaped curve in the drain pipe behind the bowl. This water does a nice job of sealing off the toilet from the noxious gases in the sewer pipe as well as keeping the bowl tidy.
When you push the tank handle, water rushes into the bowl rapidly, pushing a column of water through the entire S-shaped curve. The modern explanation is that gravity and the cohesive properties of water do the rest. Once there is a continuous column of water through the S curve, the water farthest along is falling down to the sewer. It is sticking to the water behind it and pulls it along, making the familiar whoosh sound. This flow continues until there is a break in the contiguous column of water. That break happens when the tank empties and the water in the bowl is low enough to allow air in and separate the water from itself. That is why the whoosh is followed by the gurgle. It’s the air breaking up the column of water in the S-shaped pipe. The process finishes with the water in the bowl just below the level of the top of the S-shaped pipe, ready to serve another day.
“Wait,” some might object. None of this explanation used the effect of atmospheric pressure to explain the siphon. Many of us learned that it is atmospheric pressure pushing the water over the obstacle–not cohesion pulling it along. If the cohesion argument were correct, why is the maximum height of an obstacle the siphon can pass equal to 34 feet of water, the typical atmospheric pressure? Even the ancient Greeks knew they could not siphon water out of a mine farther than 34 feet vertically. You can even calculate the maximum height of a siphon using Bernoulli’s equation and atmospheric pressure. These sure makes it look like atmospheric pressure is a key player in the operation of a siphon.
Here’s what I suspect the cohesion camp would say is happening: as the water gets higher and higher, its pressure decreases until it actually boils at room temperature. The presence of water vapor breaks the cohesion of the column of water. The argument that it is the cohesive properties of water, and not atmospheric pressure, seems to rest on a discussion of siphons in vacuum. It’s been claimed that a siphon will work even in a vacuum which would certainly remove atmospheric pressure from the explanation. So unlike Aquaman, Vacuum-man would have no problem using his toilet. (Take that, DC Comics!) But I am skeptical of this particular claim. Since water has no liquid state in vacuum, I don’t see how a vacuum siphon can even exist. The experiments the proponents of cohesion point to only put the water in the tube under vacuum, not the reservoirs. So this is not the proof that is claimed.
A physicist in Sydney shows us a pretty convincing experiment that atmospheric pressure pushes the water over the obstacle. I have not yet finished thinking about if his experiment could be explained with a cohesion argument.
At the moment, I don’t think either claim is proven…whether atmospheric pressure pushes the water up to the height of the obstacle, or whether the cohesion to water already past the obstacle pulls it along. To be a meaningful question, it must be possible to answer experimentally, at least in principle. Perhaps by studying under what conditions fluids of different cohesiveness (“tensile strength” to experts) and boiling points break the siphon the answer will be revealed. If no experiment can distinguish the two cases, even in principle, it may turn out to be just semantics. I suspect the latter. On a molecular scale, the cohesion force (created by an imbalance of electrical forces on water molecules) and the pressure force (created by an imbalance of electrical forces on water molecules) seem to me to look the same.
Regardless of whether you adhere to the cohesion or atmospheric pressure argument for driving the water over an obstacle, there is no question that is is gravity that drives the siphon. This year it was noted that even the entry for siphon was wrong in the Oxford English Dictionary (OED). The error was pointed out this summer by Australian physicist Dr. Stephen Hughes who noted:
“An extensive check of online and offline dictionaries did not reveal a single dictionary that correctly referred to gravity being the operative force in a siphon.”
New Scientist magazine combed through the history of Wikipedia entries, and they never had that wrong. (Take that, OED!)
But Aquaman is not from North America, where siphoning toilets are ubiquitous. He is from the sunken continent Atlantis, which must have evolved their own toilet technology. If a siphoning water toilet were flushed where would the water go? It would not work if the water went back directly into the same ocean. If sent elsewhere, then the toilet would continuously flush forever. But that would eventually drain the ocean. Another possibility would be to make the toilet operate with a denser fluid, such as glycol, or sulphuric acid (don’t splash). But this would only work if Aquaman somehow voided himself with fluids and other material denser than sea water, so it would not float away before flushing. Alas, some important questions are beyond the scope of even physics.