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:

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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.

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

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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! :-)

When water doesn’t seek its level

Water seeks its level. U-tube experiment. By Mirjam S. Glessmer

Last week we talked about misconceptions related to hydrostatic pressure, and how water always seeks its level. Today I’m gonna show you circumstances in which this is actually not the case!

We take the fat separator jug we used last week. Today, it is filled with fresh water, to which we add very salty water through the jug’s spout. What is going to happen? Watch the movie and find out!

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.

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

Do you see the opportunities for discussions this experiment provides? If we knew the exact volumes of fresh water and salt water, and the exact salinity, we could measure the difference in height of the water levels and try to figure out how much mixing must have taken place when the fresh water was added to the jug. Or we could use the difference in height to try and calculate the density difference between fresh water and salt water and then from that calculate salinity. So many possibilities! :-)

Water seeks its level

Water seeks its level. U-tube experiment. By Mirjam S. Glessmer

There are a lot of misconceptions related to hydrostatic pressure. One of them is that if you took a jug like the one below (or a U-tube, as in my post on letter tubes and misconceptions around hydrostatic pressure) the water level would have to be higher in the narrow snout of the jug than in the main body. So when I saw a cheap-ish fat separator jug recently, I had to get it “for my blog” (ok, because I wanted to play with it) to show that water, indeed, seeks its level.

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Fat separator jug

But it turns out it is really difficult to take pictures of the water level! My first attempt (above) was with dyed water because I thought that might make it easier to see what is going on. Turns out that the adhesion of water makes it really difficult to observe the water level: The water is pulled up along the walls of the jug, leading to these weird changes in color.

In the picture below, taken from slightly above water level, you can see the curvature of the water surface both in the main body of the jug and in the spout:

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Fat separator jug

Using clear water turns out to be the best way to photograph this phenomenon (below).

So there you see it: Water seeks its level!

Another problem with this setup is that the spout is so narrow that I am not entirely sure capillary effects don’t come into play.

One thing we can do about it: reduce surface tension by adding a little bit of dish soap!

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Fat separator jug. Water seeks its level!

Now you clearly see it. Don’t you? :-)