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In all problem involving viscosity, while applying $f=nA \frac{du}{dz}$ why do we consider velocity of the bottom layer to be zero?

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  • $\begingroup$ Technically, the content and the title of your question do not match; your title asks how it flows whereas the content asks how it doesn't flow at the boundaries. $\endgroup$
    – nluigi
    Nov 27, 2018 at 15:28

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There is something called the "no slip condition". You can read about it here:

https://www.princeton.edu/~asmits/Bicycle_web/frictionflows.html

Basically, the atomic level interactions between the fluid [that happens to be touching the solid-surface] and the solid-surface are too attractive to allow the solid-surface touching layer of the fluid to have any velocity relative to the solid-surface.

This, by the way, also holds for Couette flow: The top layer of the fluid that is in touch with the top solid-surface [plate] still has zero velocity relative to the plate (this is why the top layer of the fluid has the upper plate's velocity in Couette flow). For this to be applicable the speed of the upper plate can't be too high and you have to be in steady state, as described here:

https://en.wikipedia.org/wiki/Viscosity

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