Dynamic Viscosity Formula

Dynamic viscosity is the tangential force required to move one horizontal plane of a fluid with respect to another.

Dynamic viscosity = shearing stress / shearing rate change

The equation is written

η = τ / γ

We have:

η: Dynamic viscosity

τ: Shearing stress

γ: Shear rate

Dynamic Viscosity Formula Questions:

1) We have a fluid with a shear rate of 0.5 s^(-1) and a shearing stress of 0.76 N/m². According to its dynamic viscosity, to which one of these fluids corresponds?

water: 1 Pa*s

air: 0.018 Pa*s

mercury: 1.526 Pa*s

Answer:First calculate the dynamic viscosity using the formula above, where τ=0.76 N/m² and γ=0.5 s^(-1).

η = τ / γ

η = (0.76 N/m²) / (0.5 (1/s)) = 1.52 (N*s) / m² = 1.52 Pa*s

The fluid is mercury.

2) What is the pressure necessary to move a plane of fluid with a shear rate of 0.35 s^(-1) and a dynamic viscosity of 0.018 Pa*s?

Answer: From the formula of dynamic viscosity we can find the share stress,

τ = η * γ and then substituting the values,

τ = (0.018 Pa*s)*(0.35 s^(-1)) = 0.0063 Pa

τ = 0.0063 Pa = 0.0063 N/m²