Fluid Mechanics – Unit of dynamic viscosity (μ) in SI units Select the correct unit.

Introduction / Context:
Dynamic viscosity (μ) quantifies a fluid’s internal resistance to shear. Correct unit recognition is essential for dimensional checks in Navier–Stokes equations, pipe-flow calculations, and lubrication analyses.

Given Data / Assumptions:

• SI base units are used.
• Shear stress τ relates to velocity gradient du/dy via τ = μ * (du/dy).
• Force unit N, length m, time s, mass kg.

Concept / Approach:

From τ = μ * (du/dy), the unit of τ is N/m² (Pa), and du/dy has units s^-1. Hence μ must have units (N/m²) / (s^-1) = N·s/m² = Pa·s. This is the SI unit of dynamic viscosity. Kinematic viscosity ν equals μ/ρ and has units m²/s, distinct from μ.

Step-by-Step Solution:

Verification / Alternative check:

Common reference values: water at 20 °C has μ ≈ 1.0 × 10^-3 Pa·s = 1.0 × 10^-3 N·s/m², which is consistent with the derived unit.

Why Other Options Are Wrong:

m²/s is kinematic viscosity; Pa·s/m² introduces an extra per-area term; kg·s²/m² does not correspond to viscosity; N/m² is pressure (stress), not viscosity.

Common Pitfalls:

Confusing μ (dynamic) with ν (kinematic), or mixing SI and CGS units (e.g., poise, centipoise) without proper conversion (1 Pa·s = 10 P = 1000 cP).

Final Answer:

N·s/m²