If its "continuous flow" you wont have a cycle time :)
In any case, you will need a system capable of supplying 2750gph at whatever psi the emitters are designed to function at + enough overhead to overcome any losses due to pipe length, connections, changes in height etc.

Thanks for the post but that helped me none. And by cycle time, granted I may have used the wrong term, I am referring to the amount of time it takes the solution to go through the system and back to the reservoir. Everything you said i am aware of. If for instance it would take 15 min to recirculate the solution, than my tank size would only need to be roughly half the per hour operating volume. I was hoping to be guided in the right direction to figure this.

Its impossible to predict with any certainty as media, slope and type of system would all have a bearing. From a daily water uptake perspective that number of plants in full swing will use between 250 and 750L per day, (66-200 US gal)
The tank sizing should also take account of the EC/PH stability unless you plan to use automated adjustment.

Start with what your plants need and back it out to figure how much total volume you need as a reservoir.
Perhaps you should take one dry container saturate it with a known amount of water then see how much you recover after it is stops dripping. The difference in the two will be how much your medium holds. times however many containers you have and you have a basic volume required for each plant.
area of pipes times length gives you volume of the pipes.
add it all together and double that for container size. but for rez quantity only add 25% as starting point.
loop time is fairly inconsequential since it's a continuous cycle. you just want to make sure to keep liquid in the lines under the appropriate pressure.