Radiating sphere in higher dimensions.
 

In three dimensions, the velocity potential around a radially oscillating sphere is 1/r, where r is the radial coordinate, and the velocity is the gradient of the potential, so 1/r^2 (there's a negative sign somewhere, I guess). So if the sphere has a radially velocity of V and a radius R, then the velocity at a distance r is V*(R/r)^2.


In higher dimensions (call it N), is the velocity potential still 1/r, or does it scale as 1/(r^(N-2)) ? Is the velocity at r equal to V*(R/r)^(N-1), or are there some constants from differentiation, or does it stay the same?