A simple way to visualize how hydrostatic pressure increases with depth

I did this demo for my freediving club Active Divers (and if you aren’t following us on Insta yet, that’s what I am taking all these pretty pictures for!): 1.5l PET bottle with holes punched in every 2cm, then filled with water. Looks cool and works pretty well (except the second hole from the bottom up, which I punched in a part of the bottle’s wall that wasn’t vertical, so the resulting jet doesn’t come out horizontally in the beginning and messes up the picture. Should have thought that through before…).

Mariotte’s bottle: A nifty trick to control “reservoir height” in #dropphotography

In earlier posts on drop photography, you might have noticed that the reservoirs for the water that drops out and creates the beautiful liquid art has a weird cork on top, sealing it off, and a glass pipe sticking through. I’ve been wanting to explain what that’s all about for a while, but had to finally draw the picture for our liquid art workshop yesterday. So here we go!

Above, you see Wlodek adjusting something about it, and below is my sketch: A Mariotte’s bottle!

Very useful little thing to control pressure in a reservoir, and with pressure the “reservoir height” that is felt at the outflow, even though the reservoir height is actually changing. Basically, it’s a way to trick the system to feel a constant hydrostatic pressure.

Below on the left, you see the bottle when it has just been filled. A cork is sealing the top of the bottle, except that the inside and outside are connected by a pipe on top and the outflow at the bottom. Initially, the water level inside the top pipe and the bottle are the same and the pressure on both water surfaces is the atmospheric pressure.

As water flows out of the bottle, the water level in the bottle starts sinking. The head space (the air inside the bottle above the water) is sealed off from the outside, so as the water level sinks, its volume increases and its pressure (and thus the pressure on the water surface inside the bottle) sinks. In the middle plot below you see what happens then: The water level inside the pipe starts sinking to compensate for the missing volume inside the bottle.

Eventually, air starts bubbling out of the pipe into the headspace, and the water level inside the pipe is at the very bottom end of the pipe (right plot above). The pressure at this level (marked as A) is now atmospheric pressure, not only at the bottom of the pipe, but throughout the whole bottle. And the pressure at this level will continue to stay at atmospheric pressure levels for as long as the water level is still higher than the bottom end of this pipe. Occasionally, air will bubble out of there to compensate for further outflow.

So at the outflow, we always have the hydrostatic pressure relating to the height from B to A, no matter how much or little water there is in the reservoir. That means that all drop pictures in a series will have similar conditions, even as the reservoir is slowly getting empty. How cool is that? I love those kind of things. So simple, yet so efficient! :-)

Thank you, Archimedes!

I really like hydrostatics. Of course I like moving water even better, but even static water is great. And there are so many things to explore! If I was to teach hydrostatics any time soon, there are so many little teasers I would use.

For example this one:

A sailor is standing on the bottom step of a rope ladder, painting the outside of his ship. The bottom step is 50 cm above the water, the distance between steps is 30 cm. The flood is coming in, and the water is expected to rise by 1.5 m. How many steps will the sailor have to climb in order to keep his feet dry?

Or this one:

How much heavier will a trough in a ship lift get when a ship is inside?

A: the weight of the ship
B: the weight of all parts of the ship above the water line
C: not at all
D: I don’t know*

You might think that these are really easy questions, but then you might be surprised! Funnily enough I drafted this post weeks ago, and then last week a colleague of mine talked about how this was a really difficult question, so I had to post it now ;-)

Another question that he mentioned that students found really difficult is similar to this one:

If an anchor is dropped from a boat into a pond, what will happen to the water level?

A: It will rise
B: It will sink
C: Nothing
D: I don’t know

Answer to that one in this post

*Remember why we always include the “I don’t know” option? If not, check out some more posts on multiple choice questions under the MCQ-tag!

When diet coke cans don’t float better than regular coke cans

This is why you should always test an experiment before you run it…

On recent travels, when I saw that they were serving drinks out of tiny cans, I asked for coke and coke light, because I really like the experiment where you put two coke cans in water and the diet one floats while the regular one sinks.

Soft drinks in cans. Who knew you could do science with them?

And then I had those two new tiny cans sitting in my kitchen. My parents came over and we talked about how I am so happy I got those tiny cans, because it is less equipment to lug around when I travel to workshops or courses. And then my mom says that she has never seen the experiment for real. So of course, I have to show her. And what happens? This!

What??

Yes, the regular coke might have sunk a little deeper, but this is really not as impressive as the experiment is supposed to be!

Good thing I moved the cans (which a friend’s friend brought to Norway for me, which I then brought from Norway to Iceland and then back to Norway) with me to Germany… As you see: The large cans still show what I wanted them to show!

Better.

So who knows what is going on here? Too much head space in the tiny cans relative to the amount of soft drink they contain? New formula? Anything else?

And the moral of the story: ALWAYS try your experiments when you are using new equipment before you show them to anyone. Who would have thought that this experiment was not fail safe???