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When fluid is placed between two parallel plates such that one plate is moving and other is stationary, fluid will start flowing. Between plate and the fluid there is viscous friction given by equation: $$F = -\eta A \frac{\text{d}v}{\text{d}y}$$ where $\eta$ is fluid viscosity, $A$ is area of a plate and $\text{d}v/\text{d}y$ is a velocity gradient.

Since fluid viscosity is a measure of intermolecular or cohesive forces in a fluid, how can its value determine viscous friction between fluid and the plate since interactions between fluid and the plate aren't the same like between fluid molecules?

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The molecules of the fluid will interact with the molecules at the surface of the plate, and as a general rule this interaction is strong enough to fix the molecules of fluid to the plate and prevent them sliding over the plate. This means we effectively have a thin layer of fluid that is fixed to the plates, and any relative motion of the plates has to be accommodated by shear in the bulk of the liquid.

So when we are measuring the force needed to shear the two plates at some constant rate we can be confident that the force we measure is a property of the fluid flow, i.e. the viscosity, and not of the interaction between the fluid and the plates.

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  • $\begingroup$ Ohh, yes. No slip condition is an answer to my question because of which flowing fluid will not actually interact with the plate, but rather with itself. Thank you. $\endgroup$ Aug 4, 2021 at 15:24

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