This is not exclusive to blood or to falling into water. The issue is that a falling droplet of fluid has momentum in every portion of the fluid. When the droplet hits a fluid or surface what it is hitting doesn’t want to get out of the way so the fluid deflects, sliding along the surface until friction stops it.
The fluid can’t flow through itself so the net effect is flowing outward from the center. But remember that *all* of the fluid has momentum so fluid in the middle doesn’t want to just stop dead in place after impact. It still needs to shed speed which means it too will move away from the center.
Overall this means that if you drip even water onto the floor it tends to form a ring.
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