
strömend
pouring
Describes a liquid, especially rain, that flows in large quantities and without interruption.
Bei strömendem Regen warteten wir auf den Bus.
We waited for the bus in the pouring rain.
pouring / streaming
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pouring
Describes a liquid, especially rain, that flows in large quantities and without interruption.
Bei strömendem Regen warteten wir auf den Bus.
We waited for the bus in the pouring rain.

streaming
Describes, in a figurative sense, something that moves like a strong, continuous flow, for example light, energy, or a crowd of people.
Strömendes Licht erfüllte den Raum, als die Vorhänge aufgingen.
Streaming light filled the room when the curtains opened.
The word 'strömend' (pouring/streaming) is the present participle of the verb 'strömen' (to flow, to move in one direction). Like other participles, it can be used as an adjective to describe an ongoing action.
Die strömende Menge bewegte sich langsam in Richtung Ausgang.
The streaming crowd moved slowly toward the exit.
'Strömend' (pouring/streaming) is used almost exclusively as an adjective directly before a noun (attributively). Using it as a stand-alone predicate, e.g. 'Der Regen ist strömend' (the rain is pouring), is uncommon and sounds unnatural.
Trotz des strömenden Regens machten wir einen Spaziergang.
Despite the pouring rain, we went for a walk.
By far the most common and fixed collocation for this meaning is 'strömender Regen' (pouring rain). This combination is often used as a unit to describe heavy, continuous rain.
Wir konnten wegen des strömenden Regens nicht nach draußen gehen.
We couldn't go outside because of the pouring rain.
fluent / flowing
Fließend generally describes a liquid moving continuously. Strömend additionally emphasizes a large amount or forceful movement and is typically used in the phrase “strömender Regen” (pouring rain). Use fließend for normal continuous flow and strömend for very heavy rain or a strong flow of water.

Wir suchten Schutz vor dem strömenden Regen.
We looked for shelter from the pouring rain.
Wir reinigen die Flaschen unter fließendem Wasser.
We clean the bottles under running water.