The lift equation is valid for shallow angles of flow redirection (about ten degrees or less) in wind-tunnel confinement where lateral losses are prevented. Also it is based on a thin airfoil design of uniform curvature, adapted to circular motion in passing flow. Such is not the general case. Practical airfoils must have thickness for required strength, and must adapt to variation in curvature of flow from upwash to downwash as airspeeds and lift requirements vary. Thus circulation near a typical airfoil is distorted from circular. Farther out, at some distance, the distortion becomes insignificant. Thus assumption of circular motion passing through the calculation plane at distance, x, from the circulation center is appropriate if x is large in relation to airfoil chord. Since the magnitude of x has no effect on the final result, the equation for lift without losses can be considered valid for the general case.
In the real world of wings, lateral losses around the ends occur. Thus in application, area, the product of chord times span, is a determining factor for lift, but the ratio of span-to-chord, called aspect ratio, is also important. A higher aspect ratio means greater span and consequently greater air mass inertia opposing lateral loss around the ends.