In parallel flow, the flow velocities can be split into a u and y component the follow x and y.
The following equations can be derived for the potential
u and y-velocity
v_\infty thereby are the velocity components far enough from the regarded space that can be assumed to be constant.
\Phi(x,y) = u_\infty x + v_\infty y
\Psi(x,y) = u_\infty y - v_\infty x