Water that is not flowing could be described as 'calm' or 'still'.
How would you describe water that is flowing rapidly, but is not turbulent? (i.e. the flowing water is transparent, not white or distorted)
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If you need a purely technical term, you might try looking up laminar flow.
In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers.
P.S. I've just recalled the word unperturbed. Checking for "unperturbed stream", "unperturbed flow" on Google brings up not that many results, but let it be here, just in case.
I think "flowing" is actually the best word for your case. The word also means "with graceful movement", so that helps dispel any images of turbulent water.
Streaming or running also give the impression of water that's simply running, not rushing.
One word used as the opposite of turbulent, at least in reference to water, is "placid."
CopperKettle is correct that "laminar" flow is the technical term for the opposite of "turbulent" flow.
Laminar flow is often described as "smooth". So, if you want a less technical answer, we could say the water is clear and flowing smoothly.
I am surprised no-one has offered "quiet".
I think you could use the word, 'Trickle' in this case. Like, 'the water is flowing in a trickle,' as opposed to 'the water is gushing from the reservoir, which signifies turbulent flow.