Bath-Time Fluid Dynamics

SteelyKid’s every-so-often bath was last night, and as always, she was fascinated by scooping up water in a hexagonal cup thing that’s part of one of her bath toys, and watching it drain out. Which is completely understandable– not just because she’s a baby, but because there’s a bunch of physics at work, here.

I realize this is trampling on Rhett’s territory, but I made a little video showing the physics part (in the sink, not the tub, because I don’t want to have the pay the therapy bills that would come from posting video of SteelyKid in the tub):

The explanation is laid out in the video, but if you’re someplace where youTube doesn’t work, I’ll put a short summary below the fold:

The toy in question is a hexagonal stacking cup from a turtle-shaped bath toy:

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It has six holes in it (numbered in the picture), so it doesn’t hold water forever. One of the two physics elements to the video has to do with the draining of the cup. When the cup is full, water is pushed out through these holes by the weight of the water above the holes. When the cup is full all the way, this hydrostatic pressure is large, and the water sprays out to the side quite a bit (the holes don’t point straight down, but sideways through the wall). As the water level drops, the amount of pressure on the holes drops, and the sideways spray slows down, and eventually stops.

The really cool element, though, is that when the water flow stops completely, there’s still water in the cup above the level of the holes:

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I believe (and confidently assert in the video titles) that this is a surface tension effect. The water molecules at the surface of the water in the hole cling to one another tightly enough that the weight of the water above them (only a millimeter or so) can’t push water through the hole. So even though there’s a small hole the water could, in principle, escape through, it stays in the cup.

(The other force that might be in play here is atmospheric pressure (which is what lets you pick water up in a straw by covering one end of the straw, and also allows this trick), but I don’t think that applies to this problem, as the atmospheric pressure is the same on both sides of the hole.)

As additional evidence for this theory, if I tilt the cup sideways so all the remaining water is over just two of the holes, the flow resumes. And stops again when there is only a millimeter or so of water above the holes (though it’s much harder to see that on the video).

So, the next time you see a toddler staring fascinatedly at water draining out of something, you’ll no the reason why. It’s not just that babies will stare at anything– she’s learning physics!

Comments

  1. #1 JScarry
    May 17, 2010

    Why does the water curve inward near the end? I would have expected it to drain straight down when the pressure was too low for it to go out.

  2. #2 Rhett
    May 17, 2010

    Are you saying this is “my territory” because I like to play with toys in the tub? (who doesn’t?)

  3. #3 Zack
    May 17, 2010

    JScarry, at that point it looks to me like the water is adhering to the side of the cup right below the holes, which pulls it inward.

  4. #4 Philip
    May 17, 2010

    As I assume you are using soap in the bathwater, wouldn’t the suface tension be reduced by surfactant nature of the soap?

  5. #5 Chad Orzel
    May 17, 2010

    Why does the water curve inward near the end? I would have expected it to drain straight down when the pressure was too low for it to go out.

    As the pressure goes down, the water starts to adhere to the surface of the cup a little, and ends up rolling down to the bottom. You can see that at the end, the six streams merge into one.

    As I assume you are using soap in the bathwater, wouldn’t the surface tension be reduced by surfactant nature of the soap?

    She’s a baby, so we use relatively little soap, and very mild soap. The sink demo was done with plain water, and the water level at the end is probably a little higher as a result. It’s tough to say, though.

    I suppose I could test it multiple times with different soap concentrations, but that starts to feel like chemistry…

  6. #6 Kate Nepveu
    May 17, 2010

    Also, when Chad does this to distract her from the horrors of being put in the tub, it’s at the start when there may be a bit of bubble bath in the water, but no shampoo or soap rinsed off yet.

  7. #7 Birger Johansson
    May 17, 2010

    Regarding bathtubs: I haven’t been reading this blog before April this year, but I assume you have already adressed the myth that the vortex in a bathtub spins in a specific direction on the north hemisphere and the opposite direction on the south hemisphere (the effect only shows up at much larger scale).

  8. #8 Robert
    August 7, 2010

    You can definitely affect whether liquid will, or will not, come thru small holes in the bottom of an aluminum pie plate, by altering the liquid’s surface tension using common soaps and water.

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