A cup has approximately 4,731.76 drops of water.
The volume of the drop will depend on the dimensions of the needle or glassware and thus the number of drops will also vary.
For example, IV drips used in medicine can deliver 10, 15, 20, or 60 drops per ml.
In pharmacy, 0.05 ml is considered as the volume of a drop for usage.
Considering 0.05 ml as water drop volume, a cup (236.59 ml) will have approximately 4,731.8 drops of water.