equations for exit velocity of ball from a pipe

[winston_meerabux]

Students are doing a project. They are to build a rocket using pvc piping to propel balls using a bicycle pump. The pressure is measured using a pressure guage. They are to write equations for the velocity of the ball as it exits the pipe. Atmospheric pressure, wind velocity, static and kinetic friction, types of balls(golf,tennis, apples, potato) and any other limiting conditions that they can think of must be taken into account to develop the exit velocity of the ball. We are having a lot of arguments as to the most appropriate equation to use because the distances measured ( vertical and horizontal ) for each pressure read from the guage do not match well with the theoretical exit velocity.
We would appreciate inputs from the forum as to how best to develop a theoretical model.