hey pf! please read this, it's honestly pretty easy although long to read.(adsbygoogle = window.adsbygoogle || []).push({});

in stoke's first problem, we have parallel flow initially at rest and then, instantaneously (i know, unrealistic) one wall starts to move in the x-direction with no acceleration (yes, it magically becomes a velocity). the y-direction is perpendicular to the x direction and is directing toward the other wall. the z-direction is coming "out of the page".

okay, now time for the question.

conservation of mass for incompressible flows yields: $$ \nabla \cdot \vec{U}=0 \Rightarrow \frac{dv}{dy}=0$$ since [itex] \frac{du}{dx}=\frac{dw}{dz}[/itex] are identically zero. my question is, why isn't [itex]\frac{dv}{dy}[/itex] identically zero? i know it equals zero from the above, but how does it exist at all? how is there velocity in the [itex]y[/itex] direction?

it makes sense to me that the other two are zero by inspection, but why not [itex]y[/itex]? to me it seems [itex]\frac{du}{dy}[/itex] would not be zero but that all others would be. please help me understand how there exists y-direction velocity ([itex]y[/itex] )

thanks ahead of time!!

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# Simple question on stoke's first problem

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