Question

At a certain point in oil, the shear stress and velocity gradient are 0.2 N/m$^2$ and 0.1 s$^{-1}$ respectively, then the dynamic viscosity is

• A. 2 N-s/m$^2$
• B. 50 N-s/m$^2$
• C. 0.5 N-s/m$^2$
• D. 0.02 N-s/m$^2$

Hint:

Newton's law of viscosity, $\tau = \mu (du/dy)$, is a cornerstone of fluid mechanics.
Remember that dynamic viscosity $\mu$ is the proportionality constant between shear stress and the rate of shear strain.
Ensure your units are consistent (e.g., Pascals for stress, s$^{-1}$ for gradient) to get viscosity in Pa·s.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
τ=0.2 N/m², du/dy=0.1 s⁻¹. Find dynamic viscosity μ.

Step 2: Key Formula (Alternate):
Newton's law of viscosity: τ = μ(du/dy). μ = τ/(du/dy).

Step 3: Detailed Explanation:
μ = 0.2/0.1 = 2 N-s/m² = 2 Pa·s. Water μ≈0.001 Pa·s. This oil is 2000 times more viscous than water.

Step 4: Final Answer:
2 N-s/m².