I think the relevant equations are the divergence theorem
The Attempt at a Solution
Since it hints at a "clever" solution, I assume the difficult part is to find the right path. I think we can take advantage of the divergence theorem to convert the surface integral to a volume integral (well, it's n-dimensional, so from n-1 -> n).
I think the flux on opposite sides are canceled out, because the function is a function of radius only? But the velocity can be different on the opposite sides.
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