The flight computer shall:
- record the flight track time and altitude
- deploy the parachute
As the Arduino can readily interface with a pressure sensor to infer altitude, a servo to deploy the parachute, and has built in non-volatile memory it is well suited to this project.
An Uno has 1K of non-volatile memory, which is a little limited for data logging. However, this allows 250 time and pressure readings (at two bytes each) to be recorded. If more memory is needed, a memory card can be added.
A typical water rocket flight lasts roughly 60 seconds, most of that descending on the parachute. So, this would allow approximately 0.25 second data recording intervals, if recording starts when launch is detected. This will not yield much detail about the initial acceleration, as most of the "propellent" is consumed within 0.25 second.
The Uno has 32k of program memory, which should be plenty.