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I've got the complex potential of a flow consisting of a line sink at $z=-a$ and a line source at $z=a$ both of equal strength. I want to find the stagnation points but when I differentiate I get no solution. This is the complex potential I have got: $$\frac{Q}{2\pi}(log(z-a)-log(z+a))$$

May have got the complex potential wrong, any hints?

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    $\begingroup$ What makes you think that there is a stagnation point to begin with? Have you tried plotting the velocity field? $\endgroup$ Commented Feb 1, 2018 at 15:26

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When two "charges" are equal and opposite, there'll be no neutral point at which the electric fields from the charges balance each other. Similarly, for source and sink with equal strengths, there's no stagnation point. See more on bipolar coordinates.

If you see another case here, there'll be a neutral point such that more than one field lines meet together with other than singular points.

enter image description here

In the above case: $2Q$ and $-Q$ at $z=-1$ and $z=1$ respectively, the red curve is the equipotential whereas the blue curve is the field line such that they meet at the neutral point $z=3$.

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