1/3 of bottle volume with water, but why ?

[RaZias]

Everyone knows that 1/3 of the volume bottle with water will launch it higher. But does anyone knows why ?

I think if that question is answeared there is some improvement that could be done, like an alternative to the 1/3 water volume.

If we use a liquid 3 times more heavier than water but we put 3 times less than the water volume, there will be more air inside altough the weight of the rocket would be the same.

[Ripper]

The 1/3 water/air mix is just a rule of thumb. The actual optimal amount of water, you have to find by simulations.
The reason for the 1/3, is that the range of optimal fill ratios are usually between 20-40% water.

Basically:
The more of a rockets mass that is reaction-mass (fuel, water, air), the better it wil accelerate.
The faster this fuel is expelled, the better it will accelerate.

So:
If you fill the rocket completely with water, you'll have a heavy reaction-mass; but there will be nothing to expell it, so it will only flow out slowly.
If you don't put water in it at all, the reaction-mass will be very small (only air)

It is true that you would need a smaller volume of liquid if you use a denser liquid, but you might not get a more powerfull rocket even! The penalty of carrying a heavy liquid higher, tends to offset the gain in impulse...

Using Clifford's simulator http://cjh.polyplex.org/rockets/simulation with water and mercury at standard settings, and optimizing fill-ratio, i get
Water density 1.0:
Fill ratio: 21.4%, apogee at 77.91 meters

Mercury density 13.5:
Fill ratio: 6.2%, apogee at 67.83 meters

On a second notice: viscosity, you would need a non-viscous liquid, that is heavier than water - not easy to find - and it should be non-toxic and environmentally safe too!
Robert Youens made some experiments with his "Insane Air" rockets -(they doesn't qualify as rockets in WRA). They used Water-vapour-saturated air to a great effect. Maybe use something that is lighter than water: gasoline, freon - nah, just kidding.
My advice is: Stick to water - it's much easier to use, and safer, and cleaner, and cheaper and....

[U.S. Water Rockets1]

Everyone knows that 1/3 of the volume bottle with water will launch it higher. But does anyone knows why ?

I think if that question is answeared there is some improvement that could be done, like an alternative to the 1/3 water volume.

If we use a liquid 3 times more heavier than water but we put 3 times less than the water volume, there will be more air inside altough the weight of the rocket would be the same.

Ripper is correct about the ratio being different than 1/3. The variations in nozzle size and rocket weight and rocket pressure makes the ratio vary wildly. The only sure way to know is to establish a range of ratios with a simulator and then back up the simulation findings using real flight tests. From there you can make a spreadsheet that you can use to calibrate the output of a simulator, or you can use it to adjust the output of the simulator itself if you are good at programming.