Uniform Flow
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phi(r, theta) = (A r + B r^(-2) ) Cos(theta)
Consider the flow corresponding to n=1, A=U, B=0:
phi(r, theta) = U r Cos[theta] = U z
We see that here:
v = grad(phi) = U e_z
and therefore phi = U r cos(theta) is the velocity potential corresponding to the uniform flow of magnitude U in the z-direction.