ser-
“to flow, to move”flow, stream
Root for flowing motion, yielding Latin serum, Greek horme (impulse), Sanskrit sarati.
Discussion
The PIE root *ser- (to flow, to move in a stream) produced vocabulary for both liquid flow and human movement — a semantic unity reflecting the conceptual equation of flowing water with purposeful travel.
Latin serum (whey, watery fluid — the liquid that flows from curdled milk) continues the root in its liquid sense and gave English: serum (blood serum, the fluid component), serous (producing or containing serum), and the medical combining form sero-. The word serene (serēnus, "clear, calm" — possibly from the image of clear-flowing water, though the connection is debated) may also belong here.
Greek hormḗ (ὁρμή, "onset, rush, impulse, attack") and the related hormone (ὁρμῶν, "setting in motion" — coined 1905 by Ernest Starling for the chemical messengers that "set the body in motion") preserve the root in its human-motion sense. The Greek word for a harbour, hórmos (ὅρμος), is literally "the place where the flow comes to rest" — where ships cease their motion.
Sanskrit sárati ("he flows, he runs") continues the root transparently in the Indo-Iranian branch. The related sará- ("flowing") and sarit- ("river, stream") appear in Vedic hymns describing both literal rivers and metaphorical flows of speech and prayer.
Old Irish sirid ("he seeks, he goes") and Welsh hir ("long" — possibly from the concept of a long flow/journey) provide Celtic reflexes.
The word's dual meaning — liquid flow and purposeful motion — is not a later metaphorical development but appears to be original to PIE. The proto-speakers apparently conceived of deliberate human travel and the flow of water as aspects of the same phenomenon: continuous directed movement through space. This conceptual unity survives in modern English, where we speak of traffic flow, cash flow, and the flow of conversation using the same water metaphor.
Notes
Pokorny 909-910. English serum from Latin.