PX285 - L6 - potential flow over a wing

everywhere except the transition region, the flow is irrotational, incompressible, and follows the laplace equation
since the shape is complex, it is not analytically tractable
numerically solving the laplace equation around the aerofoil: $\nabla^{2} ϕ = 0$
the boundary conditions: $u_{⊥} = 0$ at the surface, ie: $\hat{n} \cdot u = 0$ ; $u = u_{0} \hat{i}$ , far from the aerofoil
at $A$ , since it is incompressible: $\vec{\nabla} \times \vec{u} = 0 ⟹ K = 0$ , so the net lift by magnus effect is zero
using a wind tunnel to measure the flow once it has reached a steady state, it is found that the stagnation point, $B$ , lies on the trailing edge

since there are differences in speeds, and hence pressure, there will be a lift force
this mismatch is caused by the need for considering the transition region
the transition (or boundary) region (or layer) near an object:

\frac{δ}{d} = \frac{1}{\sqrt{R e}} = {(\frac{μ}{ρ u_{0} d})}^{1 / 2}

$B$ can be moved from the potential flow pattern to the trailing edge by adding a circulation to the flow around the wing: