Dynamic (Absolute) vs. Kinematic Viscosity
Dynamic (Absolute) Viscosity — μ
Dynamic viscosity (also called absolute viscosity or static viscosity) measures a fluid's resistance
to shear — the internal force per unit area required to make one layer of fluid slide past another.
It is independent of density. The SI unit is the pascal-second (Pa·s); the common engineering unit
is the millipascal-second (mPa·s), numerically equal to centipoise (cP).
\[ \tau = \mu\,\frac{du}{dy} \]
where τ is shear stress [Pa] and du/dy is the velocity gradient [s⁻¹].
Kinematic Viscosity — ν
Kinematic viscosity is the ratio of dynamic viscosity to fluid density. It describes how easily
a fluid flows under the influence of gravity or pressure, without needing to separately account for
the applied force. The SI unit is m²/s; the common unit is mm²/s, numerically equal to centistokes (cSt).
\[ \nu = \frac{\mu}{\rho} \]
Relationship and Unit Conversion
Kinematic viscosity is derived from dynamic viscosity and density:
\[ \nu\ [\text{cSt}] = \frac{\mu\ [\text{mPa}\cdot\text{s}] \times 1000}{\rho\ [\text{kg/m}^3]} \]
Because water has a density very close to 1000 kg/m³ near room temperature, its kinematic viscosity
in cSt is numerically very close to its dynamic viscosity in cP. At elevated temperatures, water
density decreases, so kinematic viscosity diverges slightly above the cP value.
When to Use Each
Use dynamic (absolute) viscosity for: pump power calculations, pipe pressure drop
(Darcy–Weisbach), Reynolds number (Re = ρvD/μ), and any situation where force or stress is the
driving input.
Use kinematic viscosity for: gravity-driven flow, lubrication ratings, most
viscometer measurements, and flow calculations where density is already embedded in the formula
(e.g., Stokes' law, ASTM oil viscosity grades).
Note: "Absolute viscosity" and
"static viscosity" are synonyms for dynamic viscosity — they all refer to the same physical property.
"Static" distinguishes it from apparent viscosity measured at elevated shear rates in non-Newtonian fluids.
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