PX285 - L4b - aerofoil

\begin{matrix} P_{0} + \frac{ρ U_{0}^{2}}{2} = P_{T} + \frac{ρ u_{T}^{2}}{2} \\ P_{0} + \frac{ρ U_{0}^{2}}{2} = P_{B} + \frac{ρ u_{B}^{2}}{2} \\ P_{B} - P_{T} = \frac{ρ}{2} (u_{T}^{2} - u_{B}^{2}) = \frac{ρ}{2} (u_{T} + u_{B}) (u_{T} - u_{B}) ≃ \frac{ρ}{2} 2 U_{0} (u_{T} - u_{B}) \end{matrix}

L = \int_{0}^{d} (P_{B} - P_{T}) d x = ρ U_{0} [\int_{0}^{d} u_{T} d x + \int_{d}^{0} u_{B} d x] = ρ U_{B} \oint \vec{u} \cdot d \vec{l}

\vec{L} = ρ \vec{u} \times \vec{K}