If one were able to get a birds eye view of a wing - and see the the actual paths taken by he air as the wing upsets it's steady state, they woul note that the air ALWAYS takes the path(s) of least resistance.
Depending on speed and effective resistance at any given point - the air goes chordwise or bunches up and 9against the fuselage or moves spanwise around the tip.
The ideal textbook wing has no root and no tip so flow is always ideal!
Which is BS because the flow direction is constantly changing
Setting at 35000 ft on a perfectly trimmed , constant speed passenger plane - I often watched the tiny eddies along the wing making minute changes.
Which proved to me that no matter how one tries - the flow over a wingis never a 100% constant codition- so the equasions about what is happening are only true for a fixed (imaginary) condition.
But you gotta start somewhere -