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[Argument I haven't read which leads to contrary result, followed by:]
Remarks: The foregoing answer is the obvious answer, and the only answer
consistent with relativity and symmetry and other basic principles.
The foregoing simple answer does not mention the word "Bernoulli". I am
quite aware that there are more-complicated ways of analyzing the situation
that shed an interesting light on the meaning of Bernoulli's principle, and
on the rules governing correct application the principle. If somebody
wants to ask that question, we can discuss it.