Kinematic vs Dynamic Viscosity: What's the Difference and When to Use Each
You're calculating Reynolds number, and the formula needs "kinematic viscosity" - but your fluid data sheet only lists "dynamic viscosity." Or maybe it's the other way around. Viscosity notation is one of the most confusing areas in fluid mechanics for students and engineers alike. This article clears it up once and for all.
The Simple Explanation
Think of viscosity as "fluid thickness." Honey is thick - high viscosity. Water is thin - lower viscosity. Air is even thinner.
Dynamic viscosity (μ, mu) measures how hard you have to push to make the fluid slide. It's the fundamental physical property of the fluid - independent of density. Units: Pa·s (Pascal-seconds), or the older unit mPa·s (which equals centipoise, cP).
Kinematic viscosity (ν, nu) combines dynamic viscosity with the effect of density. Because denser fluids have more inertia, they need more force to overcome - kinematic viscosity captures this. It's defined as ν = μ/ρ. Units: m²/s, or the convenient unit cSt (centistoke), where 1 cSt = 10⁻⁶ m²/s.
Why Kinematic Viscosity Is Used in Reynolds Number
The Reynolds number formula is Re = ρVD/μ (using dynamic viscosity) or Re = VD/ν (using kinematic viscosity). Since ν = μ/ρ, these are mathematically identical.
The kinematic form Re = VD/ν is preferred because it's more compact and because kinematic viscosity tables are commonly available for most fluids. When you look up "viscosity of water" in an engineering textbook, the value given is usually kinematic viscosity in m²/s or cSt.
ν = μ / ρ Convert with the Kinematic Viscosity Calculator →
Reference Values for Common Fluids at 20°C
Notice that air has a kinematic viscosity 15× higher than water - even though it feels much less viscous! That's because air is so much less dense. In a Reynolds number calculation, air behaves as if it's relatively more viscous than water, which is why large air velocities are still needed to achieve the same Reynolds number as a water system.
How Temperature Affects Each Type
For liquids: both dynamic and kinematic viscosity decrease with temperature. Hot water flows more easily than cold water. This is because higher temperatures give molecules enough energy to overcome intermolecular attraction.
For gases: dynamic viscosity increases with temperature (more molecular collisions = more momentum transfer). But because gas density also decreases with temperature, kinematic viscosity increases even faster. Hot air is therefore "more viscous" in the Reynolds number sense - it produces lower Reynolds numbers at the same velocity and diameter.
Practical Tips for Engineers
- When using the Reynolds Number Calculator, use kinematic viscosity (ν) in m²/s. For water at 20°C: 1.004 × 10⁻⁶ m²/s is a safe default.
- When your data sheet only lists μ and ρ, use the Kinematic Viscosity Calculator to convert: ν = μ/ρ.
- Always use viscosity at the operating temperature, not room temperature. A 20°C error in water temperature changes viscosity by ~20%.
- For mixtures and non-standard fluids, consult a chemical engineering reference or use measurement data.
Frequently Asked Questions
Why is kinematic viscosity in m²/s? That looks like an area unit.
It does look strange! The units come from the definition ν = μ/ρ: (Pa·s) / (kg/m³) = (N/m² × s) / (kg/m³) = (kg·m/s² × s/m²) / (kg/m³) = m²/s. The "area" interpretation comes from the mathematical role of kinematic viscosity in diffusion equations - it governs how quickly momentum diffuses across a fluid.
What is the difference between centipoise (cP) and centistoke (cSt)?
Centipoise (cP) is a unit of dynamic viscosity: 1 cP = 1 mPa·s = 10⁻³ Pa·s. Centistoke (cSt) is a unit of kinematic viscosity: 1 cSt = 1 mm²/s = 10⁻⁶ m²/s. Water at 20°C has μ ≈ 1 cP and ν ≈ 1 cSt. The coincidence (both are about 1 for water) is a key reason engineers remember these values easily.
Which viscosity type does the Moody Chart use?
The Moody Chart is plotted against Reynolds number, which uses kinematic viscosity in its standard form (Re = VD/ν). So indirectly, kinematic viscosity governs where you sit on the Moody Chart. The chart itself doesn't show viscosity directly - you need to calculate Re first using our Reynolds Number Calculator.