Uniform Flow

Question

------------------------

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

Answer 1

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.