Newton’s Law of Viscosity – Relationship Between Shear Stress and Shear Rate According to Newton’s law, the shear stress on a fluid layer is directly proportional to the rate of shear strain (velocity gradient), with proportionality constant equal to the dynamic viscosity.

Introduction:
Newton’s law of viscosity provides the linear constitutive relation for Newtonian fluids, forming the basis for many laminar-flow analyses and engineering correlations.

Given Data / Assumptions:

• Simple shear between parallel plates or near a wall.
• Newtonian fluid behavior.
• Continuum hypothesis valid.

Concept / Approach:

The law states tau = mu * (du/dy), where tau is shear stress, mu is dynamic viscosity, and du/dy is the velocity gradient normal to the flow. Thus tau increases linearly with shear rate when mu is constant.

Step-by-Step Solution:

Verification / Alternative check:

Rheometer data for water and many oils produce straight-line tau vs. (du/dy) plots, confirming direct proportionality within certain ranges.

Why Other Options Are Wrong:

Equal to: Omits the proportionality constant mu. Inversely proportional or independent: Contradict the constitutive model. Logarithmic: Not applicable for Newtonian fluids.

Common Pitfalls:

Confusing Newtonian with non-Newtonian behavior (e.g., power-law fluids) where proportionality is not linear.

Final Answer:

directly proportional