Newton's law of viscosity states that the shearing stress and the rate of deformation are directly proportional through a constant of proportionality called viscosity, τ = μ du/dy, where

τ = shearing stress - N/m²

μ = dynamic viscosity - N·s/m²

du/dy = velocity gradient at y direction - 1/s

μ = dynamic viscosity - N·s/m²

du/dy = velocity gradient at y direction - 1/s

The dynamic viscosity units are N·s/m², Pa·s or kg/m·s, where

1 Pa·s = 1 N·s/m² = 1 kg/m·s

In the metric centimeter-gram-second system, the dynamic viscosity units can also be expressed as g/cm·s, dyne.s/cm² or poise (p) where

1 poise = dyne·s/cm² = g/cm·s = 1/10 Pa·s

In the industry of petroleum, centiPoise (cP) or milliPascal-second (mPa·s) is offen used as the unit of dynamic viscosity.

1 cP = 1 mPa·s = Pa·s/1000 = poise/100

The ratio of dynamic viscosity to density of the fluid is the kinematic voscosity, ν = μ / ρ, where

ν = kinematic viscosity - m²/s

μ = dynamic viscosity - 1 N·s/m² or kg/m·s

ρ = density - kg/m³

μ = dynamic viscosity - 1 N·s/m² or kg/m·s

ρ = density - kg/m³

SI uses Stokes (St) as the unit of kinematic viscosity. 1 Stokes (St) is the kinematic viscosity of a fluid with dynamic viscosity of one P and volumic mass 1 g/cm³.

1 St = 10-4 m²/s

Another frequent used unit of kinematic viscosity is Centistokes (cSt). 1 Centistokes (cSt) is the kinematic viscosity of a fluid with dynamic viscosity of 1 cP and volumic mass 1 g/cm³.

1 St = 100 cSt

1 cSt = 10^{-6} m²/s = 1 mm²/s

1 cSt = 10

The efflux time in seconds of 60 ml of fluid flowing though a calibrated Universal orifice under the coditions prescribed by test method ASTM D 88, is the Saybolt Universal Viscosity reported as Saybolt Universal Seconds (SUS) at a specified temperature.

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