Q & A: stability of water in straw

If you stick a straw into some water, cover the top of it as with your finger and remove it, water will of course stay in the bottom of the straw. But I have found that if this is done with a larger tube such as a piece of pipe, water will not stay in the bottom of it. What determines how large a tube can be used to lift water in this way?
- Richard (age 15)
San Francisco, CA USA

This is a really interesting question. There are no doubt people who know the answer in great detail, but I can at least work out a first answer approximately.

The first thing to ask is what keeps the water from dripping down? The partial vacuum on the upper part of the tube can't be the full answer, because it doesn't explain why little droplets don't simply detach from the bottom side and fall without changing the size of the vacuum. The key physical ingredient of the explanation must be surface tension, the extra free energy that's needed per area of water-air interface. Formation of a droplet increases the surface area, so unless the gravitational force is strong enough, it will take extra energy for a droplet to form, and the water will stay stuck in the tube.

How does that limit the tube radius, R? I'll do a crude calculation, not keeping track of small numerical factors, i.e. using some dimensional analysis. The extra energy required to form a drop goes as its area times the surface tension s, very roughly sR² for the biggest drop that would form from a tube of radius R. The energy lost by lowering the water in that drop by a distance comparable to its size is roughly ρgR⁴, where ρ is the mass density and g is the gravitational acceleration. So for the bottom surface of the water not to shed drops we need roughly sR²<ρgR⁴ or R²< s/ρg.

The surface tension of water near room temperature is about s= 70 ergs/cm², ρ=1 gm/cm³, g=980 cm/s², so we end up with roughly R²< 0.07 cm². That would correspond to a tube with diameter of about 4mm.  Given that I haven't tried to solve the problem exactly, that answer could easily be off by a factor of 3. Is it anywhere near the measured cutoff between tubes that hold the water and those that don't?

Mike W.

p.s. A first test showed that ~3mm diameter gave stability and ~ 10 mm diameter was unstable, so this calculation seems to be pretty close.

(published on 05/31/2012)

Why do you need cardstock to turn water upside down in a glass? If air pressure outside is stronger than the air pressure inside the cup (due to the fact that some water has fallen out creating a vacuum) then why can't you just turn water upside down in a glass without the cardstock?
- Jenna (age 24)
Sacramento, CA, USA

Hello Jenna,

This is a very interesting question! We might have seen someone doing this "magic" by turning a glass full of water upside down with a card-stock.

As you have mentioned, the trick to "magic" is that the air pressure in the atmosphere is strong enough such that it can hold the weight of the water inside the glass. However, you might have tried it out that this "magic" only works if your glass is completely full of water and you'll have to use a card-stock or something similar to cover the glass. The reason for that, even though the air pressure is strong outside the glass, there won't be any net force from the atmosphere to the water unless there's less air pressure inside the glass! That is to say if there's air in the glass, the effect due to the atmosphere outside the glass is just the same as the air inside the glass, hence there will be no excessive force due to the air pressure that can hold the water against its own weight.

Therefore, back to your original question, if we don't have a card-stock covering the glass (which effectively prevents air coming into the glass), as you turn the glass around, because water is a liquid that flows, space is created inside the glass that can let air in, which breaks the "magic". That's why we need the card-stock.

To add to what I just explained above, there is also some contribution of the surface tension of the water, which is the reason why a single piece of card-stock is able to keep the water from flowing out, because the water molecules tend to stick to each other in the surface layer of water, holding the other water molecules within the surface. However, surface tension only plays a significant role if it's not in a large scale. For example, a syringe is able to keep the liquid inside without using any cap on the tiny tube, or a straw can hold liquid with one end covered by thumb, but a cup will have to use a card-stock because the opening is too big for the surface tension to hold the water.

Therefore, due to both surface tension and the atmosphere pressure, we can turn a glass upside down while keeping the water inside.

FYI, this explanation of the pressure difference also explains why our body doesn't get crushed by the humongous atmosphere pressure. Because there is also air inside our lungs and other parts of the body, the air pressure inside is just enough to balance out that outside of our body. Hope this helps.

Lingyi

(published on 02/26/13)