Sorry about that. dP is differential pressure (or head) that the pump has to work against. The real head will be a bit more because I didn't include the hose from the pump to the cannon, but that resistance may be small depending on flow. For instance, if you used the 3mm nozzle with 1gpm or so, you could likely neglect the loss in the hose (assuming it is a reasonable diamter (say 18mm) and not very long). If you used the 18 mm nozzle and needed 36+ gpm, then you would need to include the resistance of the hose and may need to go to a larger diameter hose (such as 25 mm) to keep the resistance reasonable.
It sounds like finding a 12v DC pump that would support the 5mm nozzle might be hard to find (or may usee too much power). I think that I would start with the 3mm nozzle and see how that works for you. I bet that you will find that a decent 12v pump with the nozzle will shoot well beyond 4m.
Here is what you do for the pump selection:
1. Based on the 3mm nozzle, we know that the pump needs to do at least 1gpm (~4 lpm) when working against a head of about 2.25m. So, we know that the max flow and head of the pump need to be higher than these values.
2. Ideally, you would look up the pump curve for the selected pump and see what the pump can actually flow at that head. For instance, say you found a pump that had a max flow of 8 l/min and a max head of 4m. Although both of those number are larger than the numbers listed above, you really need to check the pump curve to know. In this case, the max flow (8 l/min) is with 0 head. At 4m head, the flow is 0. The pump curve tells you at say 2.5m head, what the pump flow will actually be. If it is greater than 4 l/min, it is okay.
3. If you can't find a pump curve, you will still be okay if the max flow and max head are well above what you need. For instance, the pump that Smooky last posted (the one that he has) is 5gpm and 35 psi (roughly 65ft of head). Because both numbers are well above what you need (1gpm, 2.25m), we know that this pump would work without even looking at the pump curve. However, it is probably more powerful than you really need, but that isn't a problem except for cost.
(The **** represents the e bay, forum won't let me post it)
Connections: - for 13mm (½") bore hose or Hep20 push-fit connectors CW193
Dimensions: - 208mm long, 160mm wide, 100mm high
Fuse Size: 10 amp
Output: 12.5 litres/minute (2.8 gallons/minute) open flow
PRESSURE SWITCH - cuts in at 1bar (15psi) - cuts out at 2.4bar (35psi)
Efficient, high-flow, self-priming pump serving 3 or more outlets
Multi-diaphragm design self primes to 1.5m vertical lift, can run dry without damage
Supplied with snap-in ports for hose or Hep20 connectors
Motor protected by automatic thermal overload cut-out
Built-in bypass valve eliminates the need for an accumulator tank
By reasonable diameter, do you mean that less than 18 mm would be too little and create too much resistance or the opposite? Maybe it's good to have at least 18 mm so that the hose fills the barrel as quickly as possible?
The description says "Multi-diaphragm design self primes to 1.5m vertical lift". Does this mean it's only got a head of 1,5m?
Last item means that it will only pull water up on the suction intake side 1.5 meters for self priming, but the discharge lift should only be limited by the motor hp, which will be building up the pressure higher as the height of the water collumn it develops will weigh more and more the higher it needs to be pumped up to. Your sketch above does not seem to be of much concern here. Your concern is that the pump should be located less than 1.5 meters above the surface of the water supply or the pump will not be able to self prime itself.
Here is my stuffy cannon using off the shelf parts. It was pretty cheap to build. i will be doing a better video of it soon.