The corrosivity of water systems varies significantly depending on many parameters including velocity (as you mentioned), temperature, impurities (especially chlorides), aeration, and pH. The recommended maximum chloride level for 316/316L at ambient temperature is about 1000 ppm so 316/316L is not used for seawater applications. Chlorides can cause pitting, stress corrosion cracking, and crevice corrosion. Acidic attack on stainless steels is very complex and depends not just on the pH but what acid is present, whether the acid is weak or strong, the type of acid (non-oxidizing versus oxidizing), the temperature, and level of dissolved oxygen. The corrosion of stainless steels by alkaline solutions is not as common or as severe as acidic attack and is not normally a problem at ambient temperature. So it is not possible to give a pH range "that 316L stainless steel can handle". Without knowing further details, a general statement can be made that the lower the pH is from neutral, the worse the corrosion whereas pH in the basic range is apt not to be an issue.
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