Dynamic viscosity (μ): select the correct SI unit.

Introduction / Context:
Dynamic viscosity quantifies a fluid’s resistance to shear deformation and appears in Newton’s law of viscosity, τ = μ (du/dy). Correct units prevent errors in calculations of laminar flow, boundary layers, and Reynolds numbers.

Given Data / Assumptions:

• Newton’s law: shear stress τ has units of force per area (N/m²).
• Velocity gradient du/dy has units of s^-1.
• Standard SI coherent unit system is used.

Concept / Approach:

From τ = μ (du/dy), rearrange to μ = τ / (du/dy). Substituting dimensions gives μ units = (N/m²) / (s^-1) = N·s/m². Since N/m² is a Pascal (Pa), μ is equivalently expressed as Pa·s. This is distinct from kinematic viscosity ν = μ/ρ with units m²/s.

Step-by-Step Solution:

Verification / Alternative check:

For water at 20°C, μ ≈ 1.002 × 10^-3 Pa·s. Converting to base SI gives ≈ 1.002 × 10^-3 kg/(m·s), consistent with the derivation.

Why Other Options Are Wrong:

(a) kg·s/m² is not dimensionally equivalent to kg/(m·s); it inverts time. (c) N·s²/m³ mismatches stress-rate dimensions. (d) m²/s is kinematic viscosity ν, not μ. (e) kg/m³ is density, another property entirely.

Common Pitfalls:

Confusing Pa·s with m²/s; mixing SI with CGS (poise, centipoise: 1 cP = 1 mPa·s).

Final Answer:

Newton·second per square metre (N·s/m² = Pa·s)