centistokes (cSt) to square millimetres per second (mm2/s) conversion

What is the centistokes?

The centistokes is a unit of kinematic viscosity, describing how readily a fluid flows under the influence of gravity by combining its dynamic viscosity and density. It is widely used in the petroleum, lubricant, and food industries because most everyday fluids fall in a convenient range when measured in centistokes.

Definition

The centistokes is one hundredth of a stokes, the CGS unit of kinematic viscosity. One stokes equals one square centimetre per second, so one centistokes equals one square millimetre per second.

$$1\ \text{cSt} = 1.00000 \times 10⁻⁶\ \text{m}^2/\text{s}$$

Equivalently, $1\ \text{cSt} = 1\ \text{mm}^2/\text{s} = 10⁻²\ \text{St}$. Kinematic viscosity is the ratio of dynamic viscosity to density: $\nu = \mu / \rho$.

Origin and History

The stokes was named after the Irish physicist Sir George Gabriel Stokes (1819–1903), whose work on fluid flow led to Stokes' law and the Navier–Stokes equations. The name was adopted within the centimetre–gram–second (CGS) system of units, and the centistokes emerged as a practical subunit because water and many light oils have viscosities near 1 cSt.

Law and Notable Facts

The stokes and centistokes are not SI units, but they remain accepted for use and are ubiquitous in industry standards such as ASTM D445 and ISO 3104. Conveniently, pure water at about 20 °C has a kinematic viscosity of very nearly 1 centistokes, making it a natural reference point.

Real-World Examples and Conversions

• Water at 20 °C: about 1.004 cSt ($1.004 \times 10⁻⁶\ \text{m}^2/\text{s}$).
• SAE 30 motor oil at 40 °C: roughly 100 cSt.
• Automotive gear oils are graded partly by their viscosity in centistokes at 100 °C.
• $100\ \text{cSt} = 1\ \text{St} = 1.00000 \times 10⁻⁴\ \text{m}^2/\text{s}$.

What is the square millimetre per second?

The square millimetre per second (mm²/s) is the practical SI unit of kinematic viscosity, numerically identical to the centistokes (cSt). It is the unit in which most liquid viscosities are quoted in engineering and lubrication data sheets.

Definition

One square millimetre per second is one millionth of a square metre per second:

$$1\ \text{mm}^2/\text{s} = 0.000001\ \text{m}^2/\text{s}$$

Because $1\ \text{mm} = 10⁻³\ \text{m}$, area scales as $10⁻⁶$, so $1\ \text{mm}^2/\text{s} = 10⁻⁶\ \text{m}^2/\text{s}$. It is exactly equal to one centistokes: $1\ \text{mm}^2/\text{s} = 1\ \text{cSt}$.

Origin and History

As the SI displaced the CGS system, the centistokes was re-expressed in coherent SI form as mm²/s, keeping the numerical values in existing tables unchanged. This convenient one-to-one equality made the transition seamless for industries such as petroleum and lubricants that had decades of data in centistokes.

Law and Notable Facts

It is a coherent submultiple within SI usage and the de facto standard for viscosity grades. ISO viscosity grade (VG) numbers, such as ISO VG 46, are defined by the fluid's mid-point kinematic viscosity in mm²/s at 40 °C — so ISO VG 46 oil is nominally 46 mm²/s at 40 °C.

Real-World Examples and Conversions

Water at 20 °C is about 1.004 mm²/s (1.004 cSt). Typical engine oil at 100 °C ranges from roughly 5 to 21 mm²/s depending on SAE grade. One $\text{mm}^2/\text{s}$ equals $10⁻⁶\ \text{m}^2/\text{s}$ and $10⁻²\ \text{stokes}$.