The immediate effect of increasing the angle of attack is that air has to double back round the trailing edge to join the rear stagnation point. This is possible for a superfluid such as liquid helium, but not for a viscous fluid like air. Instead there is a flow separation at the trailing edge and vorticity is dumped in the flow. By the topological principle of conservation of vorticity there must be extra bound vorticity of opposite rotation associated with the aerofoil, and this generates extra lift. This extra lift can be explained formally in terms of the Kutta-Joukowski circulation theorem, or informally as the Magnus effect. Note that equal transit time theory is true for liquid helium, but false for liquid sodium. No lift is generated in liquid helium.
The immediate effect of increasing the angle of attack is that air has to double back round the trailing edge to join the rear stagnation point. This is possible for a superfluid such as liquid helium, but not for a viscous fluid like air. Instead there is a flow separation at the trailing edge and vorticity is dumped in the flow. By the topological principle of conservation of vorticity there must be extra bound vorticity of opposite rotation associated with the aerofoil, and this generates extra lift. This extra lift can be explained formally in terms of the Kutta-Joukowski circulation theorem, or informally as the Magnus effect.
Note that equal transit time theory is true for liquid helium, but false for liquid sodium. No lift is generated in liquid helium.
I think the formula for lift that you've showed is wrong, because
Lift=1/2*density*area*velocity^2*Cl
You used pressure instead of density.