# Finding boundary condition of stationary solid body

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 $\textbf u \cdot \textbf n =0$?

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