Question

Determine the viscosity, in Pa-s, in between plates that has a 0.5 mm gap with each other. The moving plate travels at 0.50 m/s, relative to the stationary plate, under a shear stress of 4.0 Pa

Answer 1

Gap: $dy=0.5\ mm=5\times10^{-4}\ m$

Velocity of upper plate: $u=0.50\ m/s$

Shear stress: $\tau=4.0\ Pa$

Let the fluid viscosity between the plates be $\mu.$ We have

$$\tau=\mu\dfrac{du}{dy}$$

$du=u-0=0.50\ m/s$

Then

$$\mu=\dfrac{\tau}{\dfrac{du}{dy}}$$

$$\mu=\dfrac{4.0\ Pa}{\dfrac{0.50\ m/s}{5\times10^{-4}\ m}}=4\times10^{-3}\ Pa\cdot s$$