The nozzle spec will tell you what flow you need and at what pressure, for example, 1 nozzle rated at 10gph at 10psi would need a pump capable of generating 10gph at a 22.5ft head.
10 gal is a lot of water and thats from a single nozzle, the plants couldn`t possibly use it in an hour so running it 24/7 gives you little benefit except for heating the res.
If you put the pump on a timer, with 1 min on/4 mins off you`d still deliver 2gph per nozzle to the root chamber at the correct pressure and put 80% less heat into the res.
With a cycle time of 30 seconds on/4.5 minutes off, you`d get 1 gph per nozzle to the root chamber and the pump would run for just 6 minutes per hour.