Editing Stream function (section)

=== Effect of shift in position of reference point ===
Consider a shift in the position of the reference point, say from <math>A</math> to <math>A'</math>. Let <math>\psi '</math> denote the stream function relative to the shifted reference point <math>A'</math>:
:<math>
\psi '(x,y,t) = \int_{A '}^P \left( u\, \mathrm{d} y - v\, \mathrm{d} x \right).
</math>
Then the stream function is shifted by
:<math>\begin{align}
\Delta \psi ( t ) &= \psi '(x,y,t) - \psi (x,y,t) \\
&= \int_{A '}^A \left( u\, \mathrm{d} y - v\, \mathrm{d} x \right),
\end{align}
</math>
which implies the following:
* A shift in the position of the reference point effectively adds a constant (for steady flow) or a function solely of time (for nonsteady flow) to the stream function <math>\psi</math> at every point <math>P</math>.
* The shift in the stream function, <math>\Delta \psi</math>, is equal to the total volumetric flux, per unit thickness, through the continuous surface that extends from point <math>A'</math> to point <math>A</math>. Consequently <math>\Delta \psi = 0</math> if and only if <math>A</math> and <math>A'</math> lie on the same streamline.