River water flows fastest along the inside of a bend. Keep in mind that this is in an ideal case of a constant depth river. The depth of the water also largely affects the flow velocity, with water flowing faster in deeper areas.
Bernoulli’s principle notwithstanding, anyone who has ever piloted a canoe around a bend in a river knows that the water is effectively moving faster on the outside bend where the water is deeper and is actively eroding the bank.
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