I'm creating a super sonic ping pong ball cannon like the one recently shown on Mythbusters. I plan on using pressure rated steel pipe so it's as safe as realistically possible and showing it off at science and technology exhibits for kids. I think it will be a big hit and a great way to get kids interested in physics and science.
The device is pretty simple and well explained in this video here: https://www.youtube.com/watch?v=YYNCGZCul1Q
The key to the whole thing is ~100 psi on one side of a burst disk with a de Laval nozzle attached to a barrel on the other side. The barrel and nozzle is all in a pretty strong vacuum. The pressure chamber is using 4" pipe and the barrel is 1.5" diameter.
Since the most common usage for de Laval nozzles is in rocket motors, I ended up here. Reading and research has led me to believe that a convergent angle of 30 degrees is common in rockets. I've also read that the divergent angle of 15 degrees works but less works as well. What I can't find anywhere is the throat size.
With the goal to get the highest velocity possible using 100 PSI and 4" diameter on the convergent side and 1.5" diameter on the divergent side which is the best convergent angle, divergent angle, and most importantly, the throat diameter.
I've found equations that I think would provide this information but they are well beyond my ability to solve so any help would be greatly appreciated!