Two parallel plates, one moving at 4 m/s and the other stationary, are separated by a 5mm thick layer of oil with specific gravity of 0.80 and kinematic viscosity 1.25E-4 m2/s. What is the average shear stress in the oil? Show your work.

Average shear stress;τ = 80 Pa

Explanation:

We are given;

Thickness;t = 5mm = 0.005 m

Velocity;u = 4 m/s

Specific Gravity;Sg = 0.8

Kinematic viscosity;ν = 1.25 × 10^(-4) m²/s

We are not given density of the oil, but given specific gravity of 0.8. we know that formula for specific gravity of an object = Density of object/Density of water

Density of water = 1000 kg/m³

Thus;

0.8 = density of oil/1000

Density of oil = 800 kg/m³

Now, let's calculate dynamic viscosity of the oil. It's given by the formula;

μ = ρν

Where;

μ is dynamic viscosity

ρ is density of oil

ν is kinematic viscosity

So,

μ = 800 × 1.25 × 10^(-4)

μ = 0.1 kg/m.s

Now, formula for the average shear stress is given as;

τ = μ × u/t

Plugging in the relevant values, we have;

τ = 0.1 × 4/0.005

τ = 80 Pa