Units — dynamic viscosity (SI) Choose the correct SI unit for dynamic viscosity μ.

Introduction / Context:Correct units are critical for dimensional checks and converting between property tables. Dynamic viscosity μ and kinematic viscosity ν often get mixed up due to the variety of unit systems used in practice (SI and CGS).

Given Data / Assumptions:

• Dynamic viscosity μ relates shear stress to velocity gradient: τ = μ * (du/dy).
• Shear stress τ has units N/m^2; velocity gradient du/dy has units s^-1.

Concept / Approach:From τ = μ * (du/dy), we get μ = τ / (du/dy). Therefore μ has units (N/m^2) / (s^-1) = N·s/m^2. In SI, this is also equal to Pa·s. CGS units define 1 poise = 0.1 Pa·s and 1 stoke = 1 cm^2/s for kinematic viscosity, not dynamic viscosity.

Step-by-Step Solution:Start with τ in N/m^2 and du/dy in s^-1.Compute μ units: (N/m^2) / (s^-1) = N·s/m^2.Match this with the options → N-s/m2.

Verification / Alternative check:Use ν = μ / ρ. If μ is N·s/m^2 and ρ is kg/m^3, then ν has units (N·s/m^2)/(kg/m^3) = (kg·m/s^2 * s / m^2) * (m^3/kg) = m^2/s, confirming consistency for kinematic viscosity units.

Why Other Options Are Wrong:

• N-m/s^2 simplifies to kg·m^2/s^4, which is not viscosity.
• Poise: CGS unit for dynamic viscosity (1 P = 0.1 Pa·s), not SI base listing here.
• Stoke: CGS unit of kinematic viscosity (1 St = 1 cm^2/s), not dynamic viscosity.

Common Pitfalls:

• Confusing dynamic and kinematic viscosity units or mixing SI and CGS without conversion.

Final Answer:N-s/m2