、。
They poured water into the glass with a smooth, elegant motion.
Literal
Unhindered-[adjectival-のない], elegant gesture [with/in-で] glass [into-に] water [object-を] poured-into.
滞りのない is a set phrase — literally 'without stagnation' — used for a smooth, unbroken, effortless action. It uses ~のない (not ~がない) because it's functioning as an attributive modifier. The compound verb 注ぎ込む 'pour into' stacks 注ぐ (pour) + 込む (enter/put in) — a very productive pattern where 込む as a verb suffix adds the directional meaning 'into.' で marks manner here ('with an elegant motion').