You want a fully speed-adjustable pump for such application.
Then you can use an ESC connected to your FC to control flow of liquid depending on speed of drone.
This is required for correct spray pattern / density depending on speed flown.
Well, it depends what battery / voltage range you want to work with.
The first pump you have shown runs on 12V.(But not really suitable as discussed).
Yet the two you want to order run on 44-56V
So those wouldn’t work on a 12V /3S system.
The white and brown wire are the signal wires which will be connected directly to the FC. (Speed control wires)
Regarding pumps:
The first link/pump: 12V-Yes, speed adjustable-Yes, required pressure-No
It’s a submersible pump. So it is designed to be within a tank. Also pressure is somewhat limited and may not be enough for good spray pattern.
Second pump: It’s a air pump - not water. Also negative pressure. - Not suitable
Considerations: The reason why those other pumps you and I looked at a few days ago are of higher voltage is the fact that often heavy drones are being used in order to carry all the weight. (Weight of drone, technology, battery and the intended amount of liquid to be carried.) It is not much use having a spraying drone with only 500ml of liquid or so. Often at least 10L or more are required to do any useful spraying in agriculture. So that makes for a very heavy drone which requires lots of power to get of the ground.
That’s why you see often such drones using 12s battery banks and not just 6s or only 3s. - Hence the pumps often are rated for such voltage.
First one can be used in both ways - As a submersible or as external pump.
This can be seen in the diagram as shown on the website.
Pressure is important as the liquid will have to pushed out some nozzles in order to achieve both an even spray-pattern and large coverage. No use just squirting it out an hose.
However, whilst it would work from a flowrate, pressure and operating voltage range, I just had a look at the specs and found it is a more generic PWM signal which is used. - Not the required signal used in a flight controller. You could still use it but it will get messy as you need something like an Arduino board or so to convert the signal. So not ideal.
The Pixhawk is the device that creates the PWM signal for controlling servos, RC-switches, and ESC’s.
It is in the regular standard as required for controlling servos.
However, for decades the signal was usually based on 5-6V especially when regular batteries been used.
These days many controllers only provide 3.3V for the signal. Whilst modern equipment can handle that, older servos for example don’t like that as they still require the higher voltage.
In regards to the signal:
So in regards to that pump you’ll have two challenges in processing the signal:
a) Converting the frequency to match that pump
b) Adjusting the signal voltage to match that pump
As you’ve mentioned, easier to avoid that altogether by finding a more suitable solution.
Had a look recently in regards to suitable 12V pumps, but found old links I had for that are no longer available.
It will only change the voltage of the signal - not convert the frequency as required.
Another idea / option I cam up with:
Using a regular 12V brushless pump and attaching a ball-valve like tap which can be servo controlled. This would allow for flow to be adjusted as required depending on speed. (Control wires of servo can connect directly to FC).
Better still, if you have access to a 3D printer you could make one up with the servo directly attached to control flow of liquid.
a) Doesn’t say if brushless or not
b) It is a pump made for volume, not pressure
c) Looking at the design it may not be able to suck water up from a tank. So it would have to be mounted below or next to the tank.