How does Bernoulli's principle contribute in lifting airplane? I have searched if any explanation that bind Bernoulli's principle in lifting airplane. There is one here which receive many appreciations, but still did not answer the question. So far, it was taught, explained, or mentioned in any aerodynamic or airplane principle, but never bound the Bernoulli's formula to the lift formula. As we know, there are pressure conservation as below:
$$\mathrm{P}_{1}+\frac{1}{2} \rho \mathrm{V}_{1}^{2}+\rho \mathrm{gh}_{1}=\mathrm{P}_{2}+\frac{1}{2} \rho \mathrm{V}_{2}^{2}+\rho \mathrm{gh}_{2}$$

Due to height is considered are same below and above the wing (the different are very small), then the third part of the equation will cancel one each other. Then left only part one and part two of each side of the equation. As the velocity above (considered as V1) is said will be different below the wing which wind is faster in above, then pressure above the wing will be lower, which will lift the wing. Thats is commonly taught in every explanation. Then, the 

$$V_{2}=\sqrt{\frac{2\left(P_{1}-P_{2}\right)-\rho V_{1}^{2}}{\rho}}$$
Meanwhile, lifting formula is expressed as below:
$$L=\frac{1}{2} \rho v^{2} S C_{L}$$
V here is the airplane velocity, which is the wind hit the airfoil. Thence, V=V2 of the Bernoulli's equation above. V1 that hit upper side of the airfoils/wing, which is said faster than below, is unknown.

So, where is the Bernoulli's principle contributes in this case? How actually we calculate the lift force of an airplane?
If I understand correctly you want to know how to get from the first formula to the second one. If that is the case, the answer is simple: you don't :)

The lift formula is a simplified one, which considers the wing as a whole. It doesn't use velocities on different points of the wing, it uses the speed of the airplane. All the factors such as profile, wing shape, etc are included in the lift coefficient. This formula is useful when you already know the behavior of the wing in different situations (the behavior is determined in wind-tunnel tests or with numerical methods).