From Bernoulli's principle we know for an incompressible fluid (constant density $\rho$) in a gravitational potential $\psi=gz$, that we can state the equation along a streamline from point 1 to point 2:

$$\int\_1^2\dfrac{\partial u}{\partial t}ds+\frac{u\_2^2}{2}+\frac{p\_2}{\rho}+gz\_2=\frac{u\_1^2}{2}+\frac{p\_1}{\rho}+gz\_1.$$

Where $u\_i$ is the velocity at point $i$, $p\_i$ is the pressure at point $i$ and $z\_i$ ist the height at point $i$. 

Now lets consider an airfoil which is has no curvature at the bottom (lower camber) and has convex curvature at the top (upper camber). If we only consider stationary flow past the airfoil, we can eliminate the integral. Additionaly we assume that the change in height is small. As reference point (point 1) we take a point upstream far away from the airfoil where $p=p\_{\infty}$ and $u=u\_{\infty}$ (these values will be approximately the same for other streamlines near to that point). 

$$\frac{p\_2}{\rho}=\frac{u\_{\infty}^2}{2}-\frac{u\_2^2}{2}+\frac{p\_{\infty}}{\rho}$$

If we compare the flow above the airfoil ($2$) and below the airfoil ($2'$). We notice that the flow above has to accelerate, hence $u\_2>u\_{2'}$. Using Bernoulli's principle we can conclude $p\_2<p\_{2'}$.

**My Question:**
Is there an intuitive explanation to the relationship between faster airflow and lower pressure for this situation? This intuitive explanation should not use Bernoulli's principle or energy conservation (using pressure energy). It is not the aim to explain the generation of lift, it is to explain intuitively the relationship between velocity and pressure.

**EDIT**: 
I think I came up with an explanation. Lets imagine two particles with the same total amount of kinetic energy $T=\frac{1}{2}mv^2=\frac{1}{2}mv\_t^2+\frac{1}{2}mv\_n^2$. If a particle has higher tangential velocity $v\_t$ this implies a lower normal velocity $v\_n$. But normal velocity is a measure for pressure, because at the molecular level pressure is generated by collisions of the particles with the surface. If there is less normal velocity this implies less pressure.
Does this explanation make sense? Is there any contradiction?