The Superposition Principle

The velocity components determined from derivatives of stream function ψ (or velocity potential Φ) are linear in stream function.

As a consequence, sum of two stream functions, ψ₁ and ψ₂, is also a stream function and describes a velocity field which is vector sum of the individual fields.

For example, considering two plane flow combinatin

If,
and,

then taking  for the combination

where,