I have a ballpark figure for you, but first a couple questions and a comment or two.
Being in Kentucky, your cattle shouldn't be required to walk more then 600 feet to a water source. This can be extended up to 800 feet if the pasture is level and there is a clear line of sight to the waterer from anywhere in the pasture.
The number of waterers will depend a bit upon the flow rate of the water. I typically leave those calculations up to the engineer, but in essence, if the flow rate is too slow, you will need more waterers.
As for the number of ball waterers you should have, you should have a ball waterer for every 20-25 head within each pasture. More waterers are needed if spacing results in distances greater than 600 feet for cattle to reach a watering point within the pasture.