There isn't an area term because the foil is presumed to be infinately long so you don't have issues with air movement in the z axis.
So one of the boundary conditions is that the length considered is of unit length. So as the area equals chord x length it simplifies it down to just chord.
2D analysis of this stuff (which is what we are doing by stipulating unit length) is number crunching intensive. 3D anaylis will blow you and you computers socks off. If you then include time as well as turbulent flow you will decide sod this for a game of solders those fluids boys are off there heads I am sticking to structures and thermo things made out of steel. That fibre stuff is a pile of cack as well.
and BAOC I resent that comment, BEng Mech can do at least up to ther times 12 table.