Answer to Question #84786 in Mechanics | Relativity for Hardy

Question #84786
Q.1 Two plates of size 100 mm by 50 mm are separated with a 1 mm thick fluid in between. The top plate is moving to the right with a constant velocity of 10 m/s in response to a force of 3 N. The bottom plate is stationary. Determine the viscosity of the fluid by assuming a linear velocity distribution.
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Expert's answer
2019-02-05T11:50:44-0500

This system of two parallel plates separated by a thin layer of a fluid can be called a viscosity meter. On the one hand, the resistance provided by the fluid can be described as a shear stress:

τ=FA.\tau=\frac{F}{A}.

On the other hand, the rate of deformation is a function of distance

dd

above the stationary plate and the speed

vv

:

τ=μvd.\tau=\mu \frac{v}{d}.

Equalize:

FA=μvd,\frac{F}{A}=\mu \frac{v}{d},μ=FdAv=Fdabv=30.0010.10.0510=0.06 Pas.\mu=\frac{Fd}{Av}=\frac{Fd}{abv}=\frac{3\cdot 0.001}{0.1\cdot 0.05\cdot 10}=0.06\text{ Pa}\cdot\text{s}.

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