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A fluid flows past a stationary solid body of arbitrary shape. Write down the boundary condition on the fluid velocity $\textbf u$ for an inviscid fluid and for a viscous fluid, at the solid surface.


We learned that for fluid/solid boundary, viscous fluids, the normal and tangential components of fluid velocity at a rigid boundary must equal to those of the boundary (eg: $\textbf u =0$ on a fixed boundary)

For inviscid fluids, only the normal velocity is continuous at a boundary ($\textbf u \cdot \textbf n =0$ on a fixed boundary)


Knowing this, does that mean the answer to the question is simply $\textbf u \cdot \textbf n =0$?

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$\mathbf{u\cdot n}=0$ is indeed the answer for an inviscid fluid, and $\mathbf{u = 0}$ for a viscous one.

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