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to spill; to fall out of; to overflow
to peek through; to become visible (although normally not)
to escape (of a smile, tear, etc.)
「溢れる」 has another reading with different meanings.
コップから水が溢れてしまった。
Water spilled from the cup.
コップを傾けすぎて水が溢れた。
I tilted the cup too far and the water spilled.
大雨で川の水が堤防から溢れている。
The river is overflowing the embankment due to heavy rain.