Determining Water Ratio for Rocket Launch

[tnkfub]

Alright what i am trying to do is to find the proper ratio of water in a water bottle.

The Bottles are

591 ml

and 2 L

I am trying to figure out the equation to get the maximum height of the rocket.

Does anyone know how i can get this equation ?

i haven't factored the gravitational force that would be affecting the rocket as i am thinking it would be a constant through out the equation. If i am wrong please tell me.

I am using a standard air nozzle from a car tire to pump the air into it.

I am also thinking of making the radius of the bottle smaller inside the water bottle to have the thrust last longer. Does anyone think that's a good idea? as a smaller hole would just make the pressure release slower.

Thanks in advance

 

[minorwork]

Experiment. Try different levels. Pressure should be below burst level. Water will be about half or three fifths. Small nozzle is less reaction mass ejected thus less thrust per given pressure. Imagine a pin hole. Not much mass ejected equals less thrust. But I'll give you a link. Here. Get the water out as quick as you can, as fast as you can. But of course I wonder why you do not include gravitation. The link explains that weight of rocket diminishes as fuel leaves thus increasing acceleration.

Heat your bottle up and stretch it, make it longer, more aerodynamic.

 

[tnkfub]

So the more the thrust would give me a greater height ? The faster the water comes out would give a greater height ? than that of something a little more constant?

i think that a fraction of a difference in the radius could make a difference? that's me assuming yet i know they say don't assume.. like i am saying 3/4 is the lip of the bottle to 1/2 or 5/8

i have heated a few of the bottles and well i can't get it to shape evenly giving me one side with more weight than the other also it throws off the amount of water that's going.

I use a heat gun and a pump to make sure the pressure is outwards rather than in wards when heated.

 

[minorwork]

The bottle will not move if the thrust does not exceed the bottle's (bottle and water) weight. If the fueled bottle weighs 1 pound, a .99 pound push with your fingers can be applied all day and the bottle will go nowhere. In practice the thrust by ejecting water mass, lessens the weight to be lifted, so maybe the last bit of water ejected will lift the now lighter rocket. The link I gave in my first reply has itself a link to H2O bottle rockets. Of course the company wants money, but they have multi stage kits and varying sized nozzles for specific applications. You are correct that nozzle design is key for maximum efficiency. They have aerodynamic shaped bottles also.

You will see at this site tips for do-it-yourself modifications.
Your first two questions answers. Yes. The third is what must be maximized. Ideally as long as the water is ejected it must generate thrust higher than the combined weight of the bottle, payload, remaining fuel and "at speed" air resistance. Else it will not overcome gravity and continue accelerating against gravity. Limitations are what you seek to define.
Like Dirty Harry said, "A man has to know his limitations."
And engineers say, "You can't know your limitations until you exceed them."

Test safely. Assume that what can go wrong, will. Protect yourself. 2 liter bottles concentrate energy at pressure and can mess with your health. Wear goggles or safety glasses.

 

[clustro]

http://en.wikipedia.org/wiki/Nozzle#High_velocity_nozzles

Might want to try and fashion/find/jerry-rig a converging nozzle to the water rocket. Wikipedia says that it will accelerate subsonic fluids, increasing kinetic energy, and thus increasing velocity.

 

[minorwork]

A 2 litre bottle opening is already a converging nozzle. The best diameter though needs to be determined. The companies that sell parts have hole sizes of the nozzle varying depending on the application, ie. booster, sustainer, or water car on wheels. All are smaller than the "stock" bottle though. Diverging after constricting is efficient at supersonic ejection mass velocities. Water, though, would hug the walls of the divergent section and slow it down. Aim for what is called "laminar flow." No turbulence. A spray, instead of a clear tube of water, out of the nozzle is inefficient at sub sonic ejection mass velocities. The spray indicates thrust waste in directions not in line with the rocket axis.

 

[clustro]

that is very interesting.

Well, since in pipe flow (a nozzle is about equal to a pipe), liquids in general become turbulent with a Reynold's number above 2100.

I suppose the best way to optimize it is to try and derive an equation for the initial velocity of the rocket as a function of the air pressure immediately prior to discharge. Then, just use conservation of momentum to find the velocity of the water stream.
With that velocity, you have all the other variables accounted for except the diameter. Just set the equation for Reynold's number equal to 2100 and solve.