Hey! This is the first time I have used this forum so I hope it all goes well and I am sorry if I break any rules on my first attempt.

I have been given a question which I believe will involve quite alot of work, so I thought I would get some suggestions as to where I need to start.

Basically, I have to use a a soft drink bottle as a rocket and determine the range ignoring drag. I have been given:

Bottle Capacity: 1.25 L
Bottle Mass: 50 grams (0.050kg)
Outlet Diameter: 22 mm (0.022m) (Can be reduced to improve performance)
Compressed air
pressure inside bottle: 654 kPa (absolute)

This is purely theory it is not a practical task.

I have then been provided with Bernoulli's Equation:

pgh + 0.5pV^2 + P = constant

Where p = density, g = 9.81m/s^2, h = height, V = velosity, P = Pressure

I know I will eventually need to incorporate projectile motion equations, Ideal Gas Law and mass flows to find the range. Is there anywhere you can suggest I start as I do not want to go down the wrong path through hours of frustrating equations if it is the wrong way. I just do not know what equation flows onto the next and where to even start.

In brief:

- You can choose how much liquid vs air you put in the bottle. The optimum is about half he volume.

- Don't forget that the air gets colder as it expands to push the liquid out. So the pressure drops faster than the volume expands. Keyword "adiabatic".

- Liquid speed given by P=0.5*d*V^2 where d is its density (in consistent units...) after checking that "pgh" is negligible. And g is false anyway: replace by g + acceleration.

- Thrust is LiquidSpeed*MassPerSecond. Divide by the remaining mass of the rocket, you get its acceleration. As the ejection speed varies over time, usual rocket equations don't apply.

There are many websites about bottle rockets as this is a common activity, I suggest to visit them and look for the solution.