# Water Bottle

1. Sep 26, 2004

### Solidmozza

Today when I was toying with a water rocket I came upon a strange phenomena. The setup was like this:
I had a 625 mL coke bottle, filled half way with water. The cap had a nice hole in it, about 1.5 cm. I turned the bottle upside down, thinking that the water would just gush out, but low and behold it kept in there, only dripping once every 4 seconds or so. I tried this again, and the same result occurred
So heres my question, why did it do that? Why didnt the water just gush out at once (like it should with the force of gravity acting on it?!) What physics are involved in this?
Thanks :)

2. Sep 27, 2004

### Integral

Staff Emeritus
There are more forces then just gravity at work. The atmosphere exerts a force as well it and this is the force which keeps the water in the bottle.

3. Sep 27, 2004

### Tide

But not for too long - supporting a heavier fluid with a lighter one is intrinsicaly unstable (Rayleigh-Taylor!).

4. Sep 27, 2004

### Integral

Staff Emeritus
Humm... Humming bird feeders, pet rodent water bottles all seem to hold the water for on demand release. As long as the seal is good they retain water nearly indefinitely.

5. Sep 27, 2004

### Clausius2

First of all it seems to me that the hole is too larger for experimenting what you've said. Anyway, the water does not gush out due to the surface tension. This phenomena is typical in hydrostatics and fluids at rest, and when certain ratios between dimensions, capillarity forces and gravity forces are reached. This figures are measured by the Bond Number:

$$B_o=\frac{\sigma}{R^2 \rho g}=\frac{72.8\cdot 10^-3}{(1.5\cdot 10^-2)^2 1000 \cdot 9.8}=0.03$$

It's roughly of order 1, so that I've said I think your hole is too larger. Anyway, the force of surface tension will be approximately of the order of gravity forces in the neighborhood of the hole.

The surface tension acts like a solid membrane in the water surface. You have to push down this membrane in order to get through it. This force is balanced with the gravity force. For example, when you fill an extremely narrow pipe with water, leaving is both sections opened, and put it upside down, the fluid does not flow across the pipe due to the gravity force. By contrast, the force that counteracts the gravity is the surface tension. If you see carefully the bottom opened section of the pipe, you will see a slight curvature of the surface. This curvature balances the gravity force, "stressing" the water surface itself in order to avoid the fluid flow.

6. Sep 27, 2004

### Solidmozza

Yeah It was smaller than that, I just realised (i was estimating :tongue2: ) but thanks for that Clausius, I knew something was up!
Thanks for all the quick replies!

7. Sep 28, 2004

### Moonbear

Staff Emeritus
If the only hole is a small one at the bottom of your set-up, then air also can't get in to displace any liquid, so the liquid stays in. After a few drips, you get a lower pressure inside than outside the bottle, so the liquid stays in...or am I just stating the same thing Integral did with regard to atmospheric forces holding the water in? I'm not sure. Sorry, I can't answer with any fancy equations...I'm just a biologist :tongue2: