Question: Unidirectional flows in 2D Cartesian coordinates (also known as channel flows) are defined as systems with only one velocity component, say (v_{x}). How does the

Unidirectional flows in 2D Cartesian coordinates (also known as channel flows) are defined as systems with only one velocity component, say $v_{x}$. How does the continuity simplify for such problems? Verify that $v_{x}$ can be a function of $y$ but not a function of $x$. How does the Navier-Stokes equation simplify for such problems? How does it compare with the equations derived from a basic shell?

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