Wow, this is really great stuff man. So what is the dP exactly? Is the table based on the requirements to get the 4 m?You will need more tha 5 gpm unless you go smaller on the nozzle. The volume needs goes as the square of the diameter. For instance, if you took my original calc and used say a 9mm nozzle, the reduction in volume would be (9/18)^2 = 0.25, so about 36 gpm*.25 = 9 gpm (plus additional to cover air resistance).
With a 7mm nozzle, the required volume is (7/18)^2 * 36 gpm = 5.444 gpm. Again, this is the minimum fllow required to get the distance.
The design of most things (like this) takes some iteration. In this case, it is like this:
1. pick a nozzle size (based on what is available or how wet you want to get them)
2. calulate the volume
3. calculate the pressure drop
4. look at pump curves to see if there is a pump available (consider price, power requirements, etc) that can meet the volume minimum at that pressure drop (just looking at max flow or max head won't tell you what you need).
5. repeat steps 1-4 by adjusting nozzle size until you find something that works.
Volume is what will determine the distance with a given nozzle size. The pressure drop will be set by the design and the flow rate (friction in the line, losses at the nozzle, etc.). If I have some time later today, I will estimate the pressure drop. Do you know the diameter and length of hose from the pump to the cannon (also type of hose)?
EDIT: Here is what I came up with. This is the pressure drop for different nozzles at what I calculate for the minimum flow rate. These values assume that the pump is located 2m below the cannon and do not include the losses due to the hose. They do include pressure drop due to elevation change, acceleration, and the losses at the nozzle and at the sharp elbow at the inlet to the cannon. If you keep a small nozzle (and lower flow), the pressure drop is mostly due to elevation. It seems like if you use the 3mm nozzle, you will have the easiest time finding a pump that will work (1+ gpm at say 2.5 m head, higher numbers will work better). If you go to a larger nozzle, the pump will need more flow as well as head.
Nozzle Size (mm) min flow (gpm) min flow (lpm) dP (m) 3 1.0 3.8 2.25045 5 5.4 20.6 2.29762 7 9.0 34.0 2.56335 9 16.0 60.5 3.39408 18 36.0 136.1 7.00267