Answer to Question #84786 in Mechanics | Relativity for Hardy

Question

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.

Answer 1

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:

$$\tau=\frac{F}{A}.$$

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

$$d$$

above the stationary plate and the speed

$$v$$

:

$$\tau=\mu \frac{v}{d}.$$

Equalize:

$$\frac{F}{A}=\mu \frac{v}{d},$$ $$\mu=\frac{Fd}{Av}=\frac{Fd}{abv}=\frac{3\cdot 0.001}{0.1\cdot 0.05\cdot 10}=0.06\text{ Pa}\cdot\text{s}.$$