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
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