According to the Bernoulli's principle, an increase in the speed of a fluid causes a decrease in pressure.
In the case of an aerofoil or aircraft wing, the speed of the fluid (air) above the wing is greater than the speed below it.
But since the Bernoulli's Principle can be applied ONLY along points along the SAME streamline, how does the speed difference justify the pressure difference above and below the wing?
Best Answer
$\def\¿{\small}$Yes, Bernoulli's Theorem applies only along one streamline. It is actually a corollary of Bernoulli's theorem (or a shortcut!) that Bernoulli's Equation holds between points C and D that are not along the same streamline, subjected of course to several conditions.
$$\¿ P_{\¿C}+\frac12\rho v_{\¿ C}^2=P_{\¿ D}+\frac12\rho v_{\¿ D}^2$$(neglecting the term $\¿ \rho gh$)
The proof for this as below:
Consider the figure below.
We apply Bernoulli's Theorem to streamlines AC and BD seperately. This gives,
$$\¿ P_{\¿A}+\frac12\rho v_{\¿ A}^2=P_{\¿ C}+\frac12\rho v_{\¿ C}^2\tag{1}$$ $$\¿ P_{\¿B}+\frac12\rho v_{\¿ B}^2=P_{\¿ D}+\frac12\rho v_{\¿ D}^2\tag{2}$$
When we define points A and B to be far away from the airfoil, we can assume that $\¿ v_{\¿A}=v_{\¿B}$ and $\¿ P_{\¿A}=P_{\¿B}$. Equating equations (1) and (2) gives the initial equation.
Indeed, it's a useful corollary.
The above is a basic description about Bernoulli's theorem and airfoil. But airfoil's physics is more complicated. See this for more info.