Well, in order to get myself back into the habit of thinking about maths, I came up with this.....

(okay, actually it just came to me, and there was no real reason behind it, but if I pretend it's to help me with Uni then I feel less geeky)

There's a water cooler just outside my office, and I've been trying to work out what affects how fast the water flows out, and it's difficult. I think it's a pair of simultaneous differential equations, but it's hard to figure out.

The water is in a container of known volume

*v*, where the volume of water is

*w*, and the volume of air is

*v-w*. When water flows out, it is displaced by air, either during the water flow or after it.

As water flows out, the volume of the air in the container increases and the pressure decreases, as it expands to fill the space. Furthermore, the plastic of the container changes shape to fill the void left by the water leaving.

The point at which the air flows into the container to replace the water depends on the volume of water in the container, and presumably the speed with which the water is flowing out. It occurs when the energy required to expand the gas and collapse the plastic container becomes greater than the energy required to force a bubble up into the container past the water flowing out.

At this point, the logic could work one of two ways. The faster the water flow, the more turbulent the system and therefore less energy would be needed to push a bubble up into it. However, having said that, I have a feeling that a fast flow might well block a bubble, due to the pressure behind said flow. Not entirely sure...

The energy required to expand the air will be dependent on the volume of air present, since we are looking at a reasonably uniform volume of water exiting the system, but a variable quantity of air. When the container is full, the exit of water will require a larger degree of expansion to when the container is mostly empty, since the pressure increase is greater.

The collapsing of the plastic container will depend on the pressure of the air inside, along with the volume of water. Since the container is most pliant in the middle, this is where collapsing will take place. However, this will require more energy if it causes water displacement than if that area is filled with air.

And all these factors change as water leaves the container, and the energy required to change the air and container volume both affect the speed with which water can leave the container (by speed, I mean volume/unit time).

So we have a

*very*complex system of equations - I started off giving letters to all the variables, and then I realised that there aren't nearly enough letters - the system is in fact almost impossible to solve without a computer. And yet that's what I find myself sitting here thinking about - the mathematical physics behind water flow out of a container... :o\

Sometimes it's impossible to kid myself that I'm not a scientist...

manwhore_tma## Re:

unknownj