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Boundary Condition (No Flow Through Surface)

The fluid velocity normal to the airfoil surface must be zero. Mathematically: v⃗⋅n⃗=0\vec{v} \cdot \vec{n} = 0 on the airfoil surface.
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The statement of the theorem

The no-penetration boundary condition requires that the fluid velocity v⃗\vec{v} must be tangential to the airfoil surface S\mathcal{S} at all points. If n⃗\vec{n} is the unit normal vector to S\mathcal{S}, the condition is: v⃗⋅n⃗=0on S\vec{v} \cdot \vec{n} = 0 \quad \text{on } \mathcal{S}