"Flow" gives me an idea of peacefulness. Are you talking about a flood here? If so, I'd choose a different verb, depending on the depth and speed of the water.
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New2grammarPhilip, which preposition would you use if a bridge which is part of a street runs over the river.I think under is the best choice.
The river flows (under - I don't like under as it's too specific. How about 'past'?) the street.