Can Bernoulli's Equation be Applied Between Two Points on a Vortex Sheet?

[Mugged]

Can someone help me with this, I need to prove that a flat vortex sheet of strength $$\gamma(s)$$ at an angle of attack $$\alpha$$ with the horizontal and has a $$p_{2} - p_{1} = \rho V_{\infty} \gamma cos(\alpha)$$

I just need to mathematically manipulate 2 formulas, namely the following two:
$$\gamma = u1 - u2$$ where u1 and u2 are the tangential flow velocities above and below the vortex sheet, respectively. I know that $$V_{\infty}$$ is coming in parallel to the horizontal
Also, I need to use the Bernuolli equation: $$p_{1} + \frac{1}{2}\rho V_{1}^2 = p_{2} + \frac{1}{2}\rho V_{2}^2$$

this should be easy but i can't figure it out..any help is appreciated!

 

[ZerO LifT]

1 - Bernoulli's equation can be applied only along a stream line , can't be applied between a point these two points

2 - try to calculate the vortex strength , and integrate them to get the forces , then divide by the areas ..to get the resultant pressure.