Viscosity - Kinematic Converter

Square Meter per Second (m²/s)

The SI unit of kinematic viscosity. 1 m²/s = 10,000 stokes = 1,000,000 centistokes. Kinematic viscosity is dynamic viscosity divided by fluid density.

Scientific use: Thermodynamics, fluid dynamics, pipe flow calculations, and theoretical fluid mechanics.

Centistokes (cSt)

One hundredth of a stoke. 1 cSt = 0.01 stokes = 0.000001 m²/s = 1 mm²/s. Most common practical unit for kinematic viscosity measurements.

Widespread use: Engine oil grades (SAE), industrial oils, hydraulic fluids, and ISO viscosity classifications. Water at 20°C = 1.002 cSt (reference standard).

Stokes (St)

CGS unit of kinematic viscosity. 1 stokes = 0.0001 m²/s = 100 centistokes. Named after physicist George Gabriel Stokes. Still used in some scientific and engineering fields.

Application: Research, older technical literature, and certain scientific standards.

Square Foot per Second (ft²/s)

North American unit. 1 ft²/s ≈ 0.0929 m²/s ≈ 929 cSt. Used in US engineering calculations for pipe flow and heat transfer.

Application: American pump specifications, HVAC design, and US fluid mechanics calculations.

Square Millimeter per Second (mm²/s)

Equivalent to centistokes. 1 mm²/s = 1 cSt = 0.01 stokes. Sometimes used for precision measurements and small-scale systems.

Application: Microfluidics, precision instruments, and fine-scale engineering calculations.

Understanding Kinematic Viscosity

Kinematic viscosity accounts for both the fluid's resistance to flow (dynamic viscosity) AND its density. It's defined as:

Kinematic Viscosity (ν) = Dynamic Viscosity (μ) ÷ Fluid Density (ρ)

Why kinematic viscosity matters:

• More relevant for flow behavior in pipes and channels
• Accounts for inertial forces in addition to viscous forces
• Key to Reynolds number calculations: Re = velocity × length / kinematic viscosity
• Determines whether flow is laminar or turbulent

SAE Grades & ISO Viscosity Classes

SAE (Society of Automotive Engineers) Grades: Define kinematic viscosity at 100°C for oils

• SAE 10W: 4.1-5.5 cSt @ 100°C (W = Winter, low-temp specification)
• SAE 20W: 5.6-9.3 cSt @ 100°C
• SAE 30: 9.3-12.5 cSt @ 100°C
• SAE 40: 12.5-16.5 cSt @ 100°C
• SAE 50: 16.5-21.9 cSt @ 100°C

ISO Viscosity Classes: Industrial oils classified by kinematic viscosity @ 40°C (ISO VG 32, 46, 68, 100, 150, etc.)

Temperature Effects - CRITICAL

Kinematic viscosity is extremely temperature-dependent!

• Water: 1.787 cSt @ 0°C → 0.282 cSt @ 100°C (6× change!)
• Engine oil: 800+ cSt @ 0°C → 10-15 cSt @ 100°C (50-100× change!)
• Typical exponential relationship: viscosity roughly doubles for every 10°C drop

Always specify temperature when reporting kinematic viscosity! Oil specifications always include reference temperatures (e.g., @ 40°C and @ 100°C).

Typical Kinematic Viscosity Values (at 20°C or reference temp)

• Air (20°C): 15.1 × 10⁻⁶ m²/s (0.0000151 cSt)
• Water (20°C): 1.002 × 10⁻⁶ m²/s (1.002 cSt) - reference
• Olive oil (20°C): ~80 × 10⁻⁶ m²/s (80 cSt)
• Motor oil SAE 10W (0°C): ~1,200 cSt
• Motor oil SAE 40 (100°C): ~14 cSt
• Glycerin (20°C): ~1,500 cSt
• Honey (20°C): ~2,000-10,000 cSt
• Blood (37°C): 3.5 cSt
• ISO VG 32 hydraulic oil (40°C): 32 cSt (range 28.8-35.2)
• ISO VG 46 hydraulic oil (40°C): 46 cSt (range 41.4-50.6)

Reynolds Number & Flow Regimes

Kinematic viscosity is critical for Reynolds number calculations:

Re = (Velocity × Characteristic Length) / Kinematic Viscosity

Flow regime determination:

• Laminar flow: Re < 2,300 (smooth, organized)
• Transitional flow: 2,300 < Re < 4,000 (intermediate)
• Turbulent flow: Re > 4,000 (chaotic, mixed)

Higher kinematic viscosity → lower Re → tends toward laminar flow. This is essential for pipe sizing, heat exchanger design, and pump selection.

Key Conversion Factors & Relationships

• 1 m²/s = 10,000 stokes = 1,000,000 centistokes (cSt)
• 1 stokes = 100 centistokes = 0.0001 m²/s
• 1 centistokes = 1 mm²/s = 0.000001 m²/s
• 1 ft²/s ≈ 0.0929 m²/s ≈ 929 cSt
• Dynamic Viscosity (Pa·s) = Kinematic Viscosity (m²/s) × Density (kg/m³)
• Water @ 20°C: μ = 0.001 Pa·s, ν = 1.002 cSt (density 998.2 kg/m³)
• For temperature conversions: Use viscosity-temperature equations for accuracy