# A Doublet's stream function

We were learning about superpositions of potential flows.

so,

$$\Psi_{doublet} = \Psi_{source} + \Psi_{sink}$$

where: $$\Psi_{source} = \frac{Q'}{2\pi}\theta_1$$, and $$\Psi_{sink} = \frac{-Q'}{2\pi}\theta_2$$

I then expect: $$\Psi_{doublet} = \frac{Q'}{2\pi}(\theta_1 - \theta_2)$$

but final form we were given was, $$\Psi_{doublet} = \frac{-Q'}{2\pi}(\theta_1 - \theta_2)$$

I have no clue as to where that extra minus sign is coming from.

Thank you guys kindly for your time and help.

Seems to me that the source in this case is θ2 since the sign convention normally is -Q for inward flow. This site https://www.ecourses.ou.edu/cgi-bin/eBook.cgi?doc=&topic=fl&chap_sec=07.3&page=theory provides an example where θ2 is the source angular displacement.