**This is completely wrong. Disregard it.**After doing a similar physics problem with the Bernoulli equation for physics homework I think I have a pretty good grasp on the Bernoulli equation. This problem was notably more difficult than anything else we had done in the class, so I wondered if I was doing the right problem. Turns out that the book I was using was the second edition when they wanted the first edition. The first edition's problem was completely different (it was about an iceberg). Luckily homework isn't a big part of my grade.

Anyway, I've hashed out the differential equation for flow from a water gun in ideal conditions. This won't take into account turbulence among other things, but it's a good start. I'm going to take a shower and solve the differential equation tomorrow.

I'd post the differential equation, but you'd need a picture to go with it and an explanation, so it's really not worth posting.

With this equation you could get a rough (high) estimate for the water flow and velocity from an air pressure water gun with just a few variables. CPS will need a different, simpler equation that I could do too. The CPS equation would be less ideal than the air pressure one though because I don't exactly know how pressure in rubber CPS systems fluctuates. I know it decreases slightly, but I don't know the extent of the decrease.