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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.

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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.

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