In hydrodynamics the for a non-viscous flow the velocity (and density) fields are given by the continuity and Euler equations: $$\rho\frac{\partial \vec{v}}{\partial t}+\rho(\vec{v}\cdot\vec{\nabla})\vec{v}=-\nabla p+\rho\vec{F}_\mathrm{body},$$ $$\frac{\partial\rho}{\partial t}+\vec{\nabla}(\rho\vec{v})=0.$$
Now when we then apply this to look at simple 2D flows, we define the streamfunction $\psi(x,y)$ which is found by solving: $$\frac{\partial\psi}{\partial x}=v_y\quad\mathrm{and}\quad\frac{\partial\psi}{\partial y}=-v_x.$$ We can determine this for many kinds of flows (uniform, source, sink, vortex, ...), but when we want to look at a non-lifting flow over a cylinder we add two different kinds of flows (Source + Sink + Uniform).
Can we do this, just add the different velocity fields? I'm not sure if this is correct since the Euler equation is non-linear in the velocities ...