Units – Kinematic viscosity in SI What is the SI unit of kinematic viscosity (nu)?

Introduction:
Kinematic viscosity nu characterizes the ratio of viscous diffusion to momentum inertia and is defined as the dynamic viscosity mu divided by density rho. Dimensional clarity is important for unit conversion and checking equations in fluid mechanics and heat transfer.

Given Data / Assumptions:

• Definition: nu = mu / rho.
• Base SI units: mass kg, length m, time s.
• Dynamic viscosity mu has SI unit Pa·s = N·s/m^2 = kg/(m·s).

Concept / Approach:

Compute units: nu = (kg/(m·s)) / (kg/m^3) = (kg/(m·s)) * (m^3/kg) = m^2/s. This unit emphasizes that kinematic viscosity acts like a diffusion coefficient for momentum, analogous to thermal diffusivity alpha with units m^2/s.

Step-by-Step Solution:

Verification / Alternative check:

In CGS, the unit is cm^2/s (1 stokes = 10^−4 m^2/s). Converting confirms the SI result m^2/s.

Why Other Options Are Wrong:

N-m/s and N-m: Units of power or energy, not viscosity.N-s/m2: This is the unit of dynamic viscosity, not kinematic.kg/(m-s): Also dynamic viscosity, not kinematic.

Common Pitfalls:

Confusing mu and nu because both appear in the Navier–Stokes equations; remember nu multiplies the Laplacian in the momentum diffusion term and carries m^2/s.

Final Answer:

m2/s