Unidirectional flows in 2D Cartesian coordinates (also known as channel flows) are defined as systems with only

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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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