stokes (St) to centistokes (cSt) conversion

What is the stokes?

The stokes (St) is the CGS unit of kinematic viscosity, equal to one square centimetre per second. Its common submultiple, the centistokes (cSt), is the everyday unit for reporting the kinematic viscosity of oils and other liquids.

Definition

One stokes equals one square centimetre per second, which in SI units is:

$$1\ \text{St} = 0.0001\ \text{m}^2/\text{s}$$

Because $1\ \text{cm} = 10⁻²\ \text{m}$, area scales as $10⁻⁴$, so $1\ \text{St} = 1\ \text{cm}^2/\text{s} = 10⁻⁴\ \text{m}^2/\text{s}$ exactly. One hundredth of a stokes is a centistokes: $1\ \text{cSt} = 10⁻⁶\ \text{m}^2/\text{s} = 1\ \text{mm}^2/\text{s}$.

Origin and History

The unit is named after the Irish-British mathematician and physicist Sir George Gabriel Stokes (1819–1903), whose work on fluid dynamics includes Stokes' law for the drag on a sphere and the Navier–Stokes equations. It was introduced as the natural CGS unit for kinematic viscosity, paralleling the poise for dynamic viscosity.

Law and Notable Facts

The stokes is a CGS unit and is not part of SI, which uses m²/s. Kinematic viscosity in stokes equals dynamic viscosity in poise divided by density in g/cm³ — a clean relationship within the CGS system, since water's density is very close to 1 g/cm³.

Real-World Examples and Conversions

Water at 20 °C has a kinematic viscosity of about 0.01 St, i.e. roughly 1 cSt. One stokes ($10⁻⁴\ \text{m}^2/\text{s}$, or 100 cSt) is comparable to a moderately heavy oil. To convert, $1\ \text{St} = 100\ \text{cSt} = 100\ \text{mm}^2/\text{s}$, and $1\ \text{m}^2/\text{s} = 10{,}000\ \text{St}$.

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.
• $100\ \text{cSt} = 1\ \text{St} = 1.00000 \times 10⁻⁴\ \text{m}^2/\text{s}$.