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I came across this equation from Katz and Plotkin (1st edition, Equation 7.24),

$$q=(u^2 + w^2)^{0.5}.$$

It reads, the surface speed on the airfoil is the magnitude of the velocity. I'm wondering if this "surface speed" is the induced velocity resulting from the potential flow distribution (e.g. source, vortex) across the chord?

Thanks in advance! :)

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They are saying if you have two perpendicular velocities ($u$ and $w$), then the magnitude of the total velocity (or the surface speed) can just be determined through the Pythagorean theorem.

Really the relationship is $$q^2 = u^2 + w^2$$ where $q$ is the velocity, and $u$ and $w$ are the components of the velocity in perpendicular directions (like across the wing and down the wing).

I don't know specifically what $u$ and $w$ are in this scenario, but this question has little to do with that at the root of what is shown.

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