# 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! :-)

# Taking the hydrostatic paradox to the next (water) level

How well do people understand hydrostatics? I am preparing a workshop for tomorrow night and I am getting very bored by the questions that I have been using to introduce clickers for quite a lot of workshops now. So I decided to use the hydrostatic paradox this time around.

The first question is the standard one: If you have a U-tube and water level is given on one side, then what is the water level like on the other side? We all know the typical student answer (that typically 25% of the students are convinced of!): On the wider side the water level has to be lower since a larger volume of water is heavier than the smaller volume on the other side.

Clearly, this is not the case:

However, what happens if you use that fat separator jug the way it was intended to be used and fill it with two layers of different density (which is really what it is intended for: to separate fat from gravy! Your classical 2-layer system)?

Turns out that now the two water levels in the main body of the jug and in the spout are not the same any more: Since we filled the dense water in through the spout, the spout is filled with dense water, as is the bottom part of the jug. Only the upper part of the jug now contains fresh water.

The difference in height is only maybe a millimetre, but it is there, and it is clearly visible:

Water level 1 (red line) is the “main” water level, water level 2 (green line) is the water level in the spout and clearly different from 1, and water level 3 is the density interface.

We’ll see how well they’ll do tomorrow when I only give them levels 1 and 3, and ask them to put level 2 in. Obviously we are taking the hydrostatic paradox to the next (water) level here! :-)