I'm currently building a water rocket made out of carbon fiber pipes and fabric. Before that I built a simple water rocket made out of plastic bottles with my friend for a science competition. Now I want to take part in the science competition again but this time with my new water rocket. My friend did the height and velocity calculations for the last rocket while I was building the water rocket itself. Because of that I'm not really familiar with water rocket calculations. Of course I took a look at our old calculations but I discovered a terrible mistake. My friend just guessed the start velocity of the rocket because with the real values we'd have gotten results which would be far above the height we reached. That's also the reason why we splitted up and now I'm doing everything on my own. I looked all over the internet and in science book to find formulas with a close result to my actual height and velocity, sadly they were often too complicated and I just got into Highschool so I also didn't know if the formulas are right/verified. Can anyone recommend me formulas for the calculation of the height and velocity? I also did not find a formula for calculating the size(diameter) of my nozzle. Maybe one of you can also recommend me a formula for that. I'm really interest in rocket science and I'd love to learn more. The calculations can be complicated as long as they are close to the real height because I'm willing and ready to learn a lot about rocket science!
I'm sorry if there are some English mistakes. English is not my native language and with all these technical terms it's quite difficult for me.
I'm looking forward to your recommendations/replies!