is the unit of F hear N/m^2 for a 2D simulation? Because I have to export F from freefem++ I need to know that should I multiply it by the area of the element to have F (N) ? I am confused now.
Technically, your equation is dimensionless
I think if you redimensionalize your force with rho*U^2, you will get a N/m^3. If you multiply this with the area, you will get N/m - force per unit spanwise length - this is because the force for the three dimensional problem can be calculated with a multiplication with the spanwise length/depth.
