centistokes
Diffusivityexact by definition
The centistoke is one hundredth of a stokes, exactly 10⁻⁶ m²/s, which is identical to one square millimetre per second. It measures kinematic viscosity, the ratio of dynamic viscosity to density, and it is the unit lubricant and fuel specifications are written in. The factor is exact by definition.
Watch out: Kinematic viscosity in cSt is not dynamic viscosity in centipoise. They differ by density: \(\nu = \mu/\rho\). For water the two are numerically close because its density is near 1 g/cm³, but for oil, whose density is about 0.87, they are not, and swapping them introduces a 15% error.
| 1 cSt | 1 mm²/s |
The stokes is the CGS unit of kinematic viscosity, named for George Gabriel Stokes, and equals one square centimetre per second. The centistoke became the working unit because water at 20 °C has a kinematic viscosity of almost exactly 1 cSt, giving the scale a convenient anchor.
About the centistokes
Oil grading is done in centistokes because kinematic viscosity is what a falling-ball or capillary viscometer measures directly, and because it is what governs how a fluid behaves in a bearing film. The ISO viscosity grade system is refreshingly literal: ISO VG 46 means about 46 cSt at 40 °C, ISO VG 100 means about 100 cSt at 40 °C. Water at 20 °C is 1.0 cSt, light hydraulic oil is 20 to 50 cSt, and heavy gear oil runs into the hundreds.
Automotive grades hide the same measurement behind a different label. In a 10W-40 oil, the second number relates to viscosity at 100 °C, where the oil must still be around 12.5 to 16.3 cSt, and the "W" number relates to cold cranking behaviour at low temperature. The whole point of a multigrade is that oil thins dramatically when heated, so a straight oil is either too thick to start with or too thin to protect when hot. The measure of how much it thins is the viscosity index, computed from the cSt values at 40 °C and 100 °C, and a high index means the viscosity holds up across the range.