S04E01: The Robotic Manipulation

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?

Water sticks to itself, as shuttle astronaut Leland Melvin can see.  Blobs of water float around the space station, without diffusing into a mist, but remain cohesive.   Is this cohesion at work in a toilet flush?

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.

Gravity pulls the water (and what’s in it) down to the sewer.

“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.

21 Responses to “S04E01: The Robotic Manipulation”

  1. tudza Says:

    Aquaman does live in a dome city under the sea doesn’t he? A flush toilet would work or they might use the older method of having a seat over a trench with water running through it or they could collect it in chamber pots and dump it in a drain or trench. Process the waste water in any number of ways or just flush it out the dome waste system.

    In the ocean, outside the dome, you are in the wilderness. Fish s*** in the ocean, why not Aquaman?

  2. Uncle Al Says:

    Water on a surface is not like anything you know about water in a bucket, ditto without impurities. A capillary of degassed, particle-free (no nucleation centers) water can be pulled to the top of a sequoia. Thicker columns, defects, and dissolved air allow a gas/vapor bubble to form under rather more than an atmosphere of tension. Glassblow seal an ampoule of water under air with ullage. Seal another identical ampoule of water under its own vapor pressure, with ullage, after vigorous vacuum degassing (Vibromixer to churn).

    1) Modestly shake each. The air ampoule goes “slosh, slosh” pro forma. The vacuum ampoule goes “tinkle, tinkle” as vapor bubbles are torn in tension and implode in compression (cavitation). “Tinkle” when mixing a vacuum degas tells you the finish line is near. Water gives great tinkle.
    2) Whip each. The air ampoule goes “thunk,” impact cushioned and elasticizedby entrained air The vacuum ampoule shatters its far end then implodes backward. It’s like a lead slug landing on the far end – zero cushioning. (Lab techs: some folks read about pissing on electric fence, some folks watch it, and some folks just have to try it out for themselves.)

    Was it a boy robot hand or a girl robot hand? One does not default accept Forbidden Planet‘s Robbie’s analysis, “In my case, sir, the question is totally without meaning.” Amy Farrah Fowler’s three-figure brain zowies (re electronic addicts, “elads,” in Larry Niven’s alternate futures) recall simulated drops re the Marine lieutenant in Aliens. It did not turn out well for the platoon, though the lieutenant did buy into redemption.

  3. Paul Dushkind Says:

    Once again, I’m astonished by how little scientists understand some mundane things. We can send a man to the moon, but we don’t know how a toilet works. We also don’t know at what speed it’s most fuel-efficient to close the car window and turn on the air conditioner.

    • Anonymous Says:

      Why is this so astonishing? Engineering something to flush or land on the moon is very different than “understanding” the flushing or landing. Newtonian physics got us to the moon and that still is based on ether-transmitted gravity. Hell, we still don’t really understand wtf is electricity and yet we still have iphones and light bulbs.

  4. Chris Says:

    What if we did this exp with mercury in a vacuum? It would be a liquid, although the cohesive properties are different.

    • David Saltzberg Says:

      I was thinking of that, but I’m not sure that mercury is a liquid in a vacuum. It has a low vapor pressure at room temperature, 1.2umHg, to be sure. But not zero.

  5. Jesse Says:

    The toilet could also work with a less dense fluid and low density excreta if he merely sat upside down. You’re showing your surface-dwelling bias!

  6. phil Says:

    Aquaman could go to the toilet in the ocean the same way every other marine mammal (dolphin, whale, manatee, etc.) does it – they just pull down their pants, “do their business”, pull their pants back up and swim away discretely and ignore the signs which say “No Peeing in the Ocean.” Well, maybe the other mammals don’t have to worry about their pants.

    My bigger gripe in the episode was Sheldon’s assumptions when calculating the number of men Penny has dated. He says he’s known her for three years and she was single for two of them (the other year was when she was dating Leonard exclusively). He then makes the assumption that from age 16 (corrected to 14 by Penny) until he met her that she was not in any long term relationships with a single guy, and makes his projections based on that postulate.

    Is that realistic? We know that Penny was serious about dating Kurt for a while and it’s quite possible she had other long term relationships in the past which would dramatically reduce both the number of men she’s dated and the number of men she’s slept with.

    • David N. Andrews M. Ed., C. P. S. E. Says:

      It’s as realistic as any estimate could be, given the available data (which – as far as I can tell – is caveated in the programme). Remember, he said he was extrapolating on the data he had observed.

      Of course – he could have asked Penny 🙂

  7. mae c Says:

    wow this is great, i just started watching season 3…haha too late i gues 😀

  8. AquamanFan Says:

    Just found this amazing website. The best science blog of all time! Please keep up the good work.

  9. feldfrei Says:

    Hi David,

    that’s indeed an interesting question. I have some idea (which I hope is not complete nonsense) which may be more like a Gedankenexperiment but may work in reality in order to decide whether it’s pressure or cohesion (or both). First of all, we need cohesion per defintionem to have a liquid (including surface tension – when the internal thermal motion overcomes cohesion at the “critical point” there’s not liquid phase anymore). Cohesion is in a sense helpful for the syphon since it helps the liquid to seal the pipe. This reminds me the idea that air pressure can keep water inside an inverted glass of water … if there wouldn’t be the hydrostatic instability (a piece of not too thin paper helps). Surface tension can also help if the area is not too large – an example is the klepsydra (as e.g. described in Carl Sagans famous book ‘Cosmos’). But let’s stop these side remarks and come to the point…

    Assume we have a working syphon through which water is transported over a barrier height h. Now the whole device is placed inside a vacuum vessel and the air starts to be pumped out. Once the pressure falls below rho*g*h (rho the density of the liquid) the syphon will break: either due to insufficient pressure (as the pressure fraction would argue) or because the liquid starts to boil at the uppermost part of the syphon. And here comes the point: real liquids can stay in the liquid phase even above boiling temperature and, hence, also below its vapour pressure – a phenomenon which is known as superheating. This should allow to distinguish both mechanisms discussed above. The pressure mechanism should stop when the pressure drops below rho*g*h, whereas the cohesion mechanism (which treats the liquid column inside the pipe as a chain) should still work as long as no vapour bubble breaks the syphon – which may be prevented at least for some time by superheating.

  10. Gillian Colclough Says:

    What fun it is to come into work at our university and find kindred kin theorsising about the scientific principles that underlay last night’s (E1 in Australia) episode. In my case, there is no science or maths with meaning at the time, but it’s all fun and I make sense of it here. However, David, you have seriously upset my emotional equilibrium by giving Wikipedia academic credibility. As for New Scientist – well, that’s it. No more contributions to their wealth from me. Enjoy your day. I will spend mine huddled in a corner and shaking as I repeat to a horde of imaginery students ‘no, you cannot cite Wikipedia; no, you cannot…’

    • David Saltzberg Says:

      No need to fight wikipedia. For a recent undergraduate seminar class, I had the students write their own (new) wikipedia articles. That’s better than having them write an essay nobody but me would read. It’s fun to watch an entry evolve. It gives the students a window onto how the sausages are made.

  11. discodave Says:

    Raj should’ve asked Howard, he’s the one who knows the answer. Howard designed a space toilet and he understands how to make Aquaman’s toilet work too.

    Aquaman’s toilet would be like the space toilet; a suction system would pull the ambient fluid (air or seawater) down into the toilet. When designed properly, the flow of the ambient fluid entrains the waste and carries it toward the collection and treatment system. This requires active pumping, it would not work during a power blackout, and the pumps creating the suction would need maintenance – but it is a working solution.

  12. Rodger Says:


  13. Tradução: “S04E01: The Robotic Manipulation (A Manipulação Robótica)” « The Big Blog Theory (em Português!) Says:

    […] feita por Hitomi a partir de texto extraído de The Big Blog Theory, de autoria de David Saltzberg, originalmente publicado em 23 de Setembro de […]

  14. leo Says:

    If a 30cm wide pipe was at open at one end of a natual under water sea current and the other end was open to the same current area in the opposite direction, the middle of this tube could have a toilet seat like opening with a rubber seal edge which when opened and sat on you could do your ablutions ( you would wait till everything is washed away , a natual bidèt),Aquaman could have a toilet. As long as a filter was used all beaches on earth could have these type of toilets installed 😉 .I know people will just do it straight in the sea just like all swimming pools on earth ewe!

  15. leo Says:

    and no moving parts for Aquaman toilet very efficient.

  16. Blog ALL » TBBT第4季1集:虹吸马桶 Says:

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