The math of one lap
The end tower travels the circumference, 2 x pi x radius. Divide that by its speed and you get the time for one revolution.
During that time the pump delivers flow x time liters. Spread over the circle's area (pi x radius squared), liters per square meter is the same as millimeters of water. So depth = flow x time / area. This is the bookkeeping irrigation designers use, simplified here by ignoring evaporation and wind drift and treating the end gun area as part of the circle.
Why the outer sprinklers work harder
Each meter of pipe near the end sweeps a much bigger ring of field than a meter near the center. Designers fit bigger nozzles toward the outer end so every part of the circle gets about the same depth. Watching the outer ring is a good check on uniformity.