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.
