Question

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

With linear velocity distribution a shear stress in a fluid equals

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

For all Newtonian fluids the shear stress depends on a coefficient of viscosity

$$\mu$$

, velocity of a flow

$$v$$

, and the height

$$h$$

above the fixed surface (plate):

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

Find the viscosity from these two expressions:

$$\frac{F}{ab}=\mu\frac{v}{h},$$ $$\mu=\frac{Fh}{abv}=\frac{3\cdot 0.001}{0.1\cdot 0.05\cdot 10}=0.06\text{ Pa}\cdot\text{s}.$$