In Newton’s viscosity relation τ = μ (du/dy), the symbol μ represents which property of the fluid?

Introduction / Context:Precise terminology matters in fluid mechanics. Newton’s law of viscosity defines a proportionality constant between shear stress and velocity gradient. This constant has standard names and units that distinguish it from other viscosity measures.

Given Data / Assumptions:

• Shear stress τ is proportional to du/dy for Newtonian fluids.
• SI units are used unless otherwise stated.

Concept / Approach:In τ = μ (du/dy), μ is the dynamic (also called absolute) viscosity, with SI unit Pa·s (N·s/m^2). The kinematic viscosity is ν = μ/ρ with units m^2/s. Vague terms like “simple viscosity” or just “viscosity” can cause confusion in calculations and unit checks.

Step-by-Step Solution:Identify the equation as Newton’s law of viscosity.Recognize μ as a property independent of the shear rate for Newtonian fluids.Select the precise term “dynamic viscosity”.

Verification / Alternative check:Dimensional analysis: [μ] = [τ]/[du/dy] = (N/m^2) / (s^-1) = N·s/m^2 = Pa·s, confirming dynamic viscosity, not kinematic viscosity.

Why Other Options Are Wrong:“Viscosity” and “simple viscosity” are imprecise; “absolute viscosity” is acceptable but the best standard term is dynamic viscosity.“All of the above” would imply every label is equally correct, which is misleading.

Common Pitfalls:

• Mixing ν and μ in formulas (e.g., Reynolds number uses ν).
• Assuming μ is constant for non-Newtonian fluids.

Final Answer:Dynamic viscosity