Dynamic and Kinematic Viscosity Explained
Viscosity describes how resistant a fluid is to shearing forces. The two standard measures address different physical questions.
- Dynamic viscosity (measured in poise, P) quantifies the force needed to move a fluid at a given velocity. If you're pumping oil through a pipe or squeezing toothpaste from a tube, dynamic viscosity governs the effort required.
- Kinematic viscosity (measured in stokes, St) accounts for both resistance and the fluid's inertia—essentially, how fast the fluid flows under gravity alone. It's dynamic viscosity normalised by density.
Both metrics are essential in different fields. Lubricant manufacturers specify dynamic viscosity for machinery protection. Hydrologists and chemical engineers often work with kinematic viscosity because it cancels out density variation and depends only on molecular interactions.
The Conversion Formula
Kinematic and dynamic viscosity are linked through a single, straightforward relationship:
ν = η / ρ
ν— Kinematic viscosity in stokes (St)η— Dynamic viscosity in poise (P)ρ— Fluid density in grams per cubic centimetre (g/cm³)
Worked Example: Converting Water Viscosity
Consider water at 20°C, a standard reference point in fluid mechanics:
- Density: ρ = 0.9982 g/cm³
- Dynamic viscosity: η = 0.010016 poise
Applying the formula:
ν = 0.010016 P ÷ 0.9982 g/cm³ = 0.010034 St
Expressed in centistokes (cSt), a more practical unit for low-viscosity liquids: 1.0034 cSt. This value matches tabulated water viscosity data, confirming the calculation.
Reverse Conversion: Stokes to Poise
To convert from kinematic viscosity back to dynamic viscosity, simply rearrange the formula by multiplying instead of dividing:
η = ν × ρ
For example, diesel fuel with kinematic viscosity 0.025 St and density 0.90 g/cm³:
η = 0.025 St × 0.90 g/cm³ = 0.0225 poise
This reverse relationship is equally valid and commonly used when specifying lubricant requirements across different temperature ranges.
Common Pitfalls in Viscosity Conversion
Accurate conversions require attention to density units and understanding the temperature-dependency of both properties.
- Density Units Must Match — Always ensure density is in g/cm³ when using this formula. If you only have density in kg/m³ (the SI unit), divide by 1000 first. Mixing units—say, density in kg/m³ with viscosity in poise—produces incorrect results by a factor of 1000.
- Temperature Dramatically Changes Viscosity — Both dynamic and kinematic viscosity are extremely temperature-sensitive. Water's dynamic viscosity halves between 20°C and 60°C. If you're working with industrial fluids, always specify the temperature at which viscosity was measured. Temperature-corrected viscosity charts or density tables are essential.
- Density Variation at Different Temperatures — Fluid density itself varies with temperature, though usually less dramatically than viscosity. For precise conversions spanning a wide temperature range, you may need separate density and viscosity values at your specific temperature, not just reference values.
- Centistokes (cSt) vs Stokes (St) — In practice, 1 St = 100 cSt. Most industrial fluids (oils, syrups) have kinematic viscosities in the cSt range. Accidentally confusing these units or forgetting to convert when reporting results leads to off-by-a-factor-of-100 errors.