Stokes (St): CGS Unit of Kinematic Viscosity

Definition and Unit Relationships

Kinematic viscosity ν measures the ratio of dynamic viscosity μ to mass density ρ, following ν = μ / ρ. In the CGS system, μ is measured in poise (P) and ρ in grams per cubic centimetre. One stokes equals one square centimetre per second (1 St = 1 cm²/s). Expressed in SI units, 1 St = 10⁻⁴ m²/s. The centistoke, common in lubrication specifications, equals 10⁻⁶ m²/s. Because industrial practice often quotes densities in kilograms per cubic metre and viscosities in pascal-seconds, careful unit conversion ensures ν remains coherent. For example, a lubricant with dynamic viscosity 0.25 Pa·s and density 860 kg/m³ has kinematic viscosity ν = 0.25/860 ≈ 2.91×10⁻⁴ m²/s, or 2,910 cSt.

ISO 80000-4 designates kinematic viscosity with the symbol ν and emphasises SI coherence, yet it recognises that industries may report data in stokes due to legacy test methods such as ASTM D445 and ISO 3104. These standards provide canonical procedures for measuring kinematic viscosity using glass capillary viscometers and specify how to report results with expanded uncertainty. When communicating across disciplines, always pair stokes values with SI equivalents to avoid ambiguity.

Historical Context and Adoption

George Gabriel Stokes and the diffusion analogy

George Gabriel Stokes, the nineteenth-century Irish mathematician and physicist, developed the foundational equations of viscous flow while studying the motion of pendulums in fluids and the settling of particles. His 1851 treatise introduced what later became known as Stokes’ law for drag on small spheres and framed viscosity as a diffusion process analogous to heat conduction. The stokes unit honours this conceptual bridge. Early meteorologists adopted the unit to describe eddy viscosity in the atmosphere, while lubrication engineers used centistokes to specify oil grades long before SI rationalisation.

Persistence in engineering standards

Despite the 1960 creation of the SI, the stokes persists in numerous technical documents. ASTM D2270 references kinematic viscosity in centistokes when calculating the Viscosity Index of lubricating oils. Aviation turbine fuel specifications (ASTM D1655) cite maximum viscosities in both mm²/s and cSt, effectively identical units. Maritime diesel engine manuals continue to list heater settings in centistokes to match existing viscosity-temperature charts. The coexistence of CGS and SI units requires practitioners to master conversion factors and document their calculations clearly to maintain compliance with ISO 9001 quality systems.

Measurement Techniques and Traceability

Laboratory measurement of kinematic viscosity often employs glass capillary viscometers (Ubbelohde, Cannon-Fenske, or Zeitfuchs). A fluid sample flows between two marks under gravity, and technicians record the efflux time using thermostatically controlled baths. The kinematic viscosity equals the product of efflux time and a calibration constant, typically yielding results in mm²/s, numerically equivalent to cSt. Calibration constants derive from certified reference materials (CRMs) whose viscosities are traceable to national metrology institutes. Reporting includes bath temperature, efflux time, viscosity, and expanded uncertainty U with coverage factor k = 2.

Emerging techniques such as oscillating piston viscometers and microfluidic rheometers extend measurement capability to high-pressure or small-volume samples. These instruments usually output SI units directly but may allow user-selected displays in cSt for compatibility with historical datasets. When adopting new technology, verify that the instrument’s firmware applies correct density compensation if it reports both dynamic and kinematic viscosity. Cross-checking results with traditional glass viscometers reinforces confidence in the measurement chain.

Using Stokes in Analysis and Design

Lubrication and tribology

Lubricant selection hinges on kinematic viscosity at operating temperature. Engineers consult viscosity-temperature charts expressed in centistokes to determine whether hydrodynamic films remain thick enough to separate surfaces. Gearboxes, hydraulic systems, and journal bearings specify minimum and maximum ν values to ensure adequate lubrication and manageable pumping losses. When translating these requirements into SI-based simulations, convert cSt to m²/s and pair the data with density profiles. The dynamic viscosity article explains how μ and ν interact in bearing design calculations.

Meteorology and environmental science

Atmospheric scientists describe eddy viscosity in stokes or m²/s to model turbulent diffusion of momentum. Planetary boundary layer schemes within weather and climate models adjust ν to simulate stability-dependent mixing. In air-quality studies, kinematic viscosity influences pollutant dispersion and the settling velocity of aerosols. Converting stokes to SI units ensures compatibility with other transport coefficients, particularly when coupling atmospheric models with ocean circulation codes that share numerical solvers.

Chemical and process engineering

Polymer processing, food manufacturing, and wastewater treatment often rely on empirical correlations that expect ν in centistokes. For example, Stokes’ law predicts terminal settling velocity v_s = (2/9)·(ρ_p − ρ)·g·r²/μ. Expressing μ as ρ·ν highlights the role of kinematic viscosity. Process engineers combine ν with characteristic lengths and velocities to compute Reynolds numbers and transition thresholds. Use our Reynolds number calculator after converting stokes to m²/s to verify laminar or turbulent regimes in pipelines and reactors.

Conversions, Reporting, and Best Practices

Maintain clarity by documenting the unit used alongside every viscosity value. When presenting data, specify temperature because ν varies strongly with thermal conditions. For quick conversions, remember that 1 cSt = 1 mm²/s = 10⁻⁶ m²/s. Many laboratories provide digital certificates including both SI and CGS units to satisfy auditors. When using software that assumes SI units, input ν in m²/s to avoid errors. If the source data are in stokes, multiply by 10⁻⁴ before entering them. Conversely, dividing m²/s values by 10⁻⁴ returns stokes, and by 10⁻⁶ returns centistokes.

Communicate uncertainty by following ISO Guide 98-3 (GUM). Include repeatability, bath temperature stability, and calibration constant uncertainty in the budget. When referencing legacy documents, confirm whether “SSU” (Saybolt seconds universal) or Engler degrees appear; these viscosimeter-specific units require conversion tables to yield stokes or SI values. Cross-reference the poise article to ensure dynamic and kinematic viscosities remain consistent.

Why the Stokes Still Matters

The persistence of the stokes reflects its practical utility in industries with decades of historical data. Lubricant manufacturers, standards bodies, and regulatory agencies continue to publish charts, specifications, and compliance forms in centistokes. Engineers who understand both CGS and SI frameworks can translate these documents without losing nuance, ensuring compatibility between lab measurements, simulation tools, and field operations. Mastery of the stokes also simplifies collaboration with partners who rely on legacy reporting systems.

Ultimately, kinematic viscosity underpins how fluids flow, mix, and transport momentum. Whether you are calibrating a capillary viscometer, modelling atmospheric turbulence, or tuning a hydraulic system, recognising the relationships between stokes, poise, and SI units keeps calculations grounded in physical reality. Continue exploring with the Reynolds number guide and the Prandtl number explainer to integrate viscosity data into broader transport analyses.