centistokes (cSt) to square metres per second (m2/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 metre per second?

The square metre per second (m²/s) is the SI derived unit of kinematic viscosity and of diffusivity. Kinematic viscosity is the ratio of a fluid's dynamic viscosity to its density, describing how readily a fluid flows under gravity independent of its mass.

Definition

One square metre per second is the SI coherent unit of kinematic viscosity, obtained by dividing dynamic viscosity (Pa·s) by density (kg/m³):

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

Equivalently, $1\ \text{m}^2/\text{s} = 1\ \text{Pa·s} \div 1\ \text{kg/m}^3$. Its dimensions are area per time (L²T⁻¹). The same unit measures mass diffusivity and thermal diffusivity.

Origin and History

The concept of kinematic viscosity was developed in fluid mechanics to separate a fluid's resistance to shear (dynamic viscosity) from the inertial effect of its density. The SI adopted the coherent unit m²/s as part of the metre-kilogram-second framework, replacing the older CGS stokes (cm²/s).

Law and Notable Facts

The m²/s is the SI-preferred unit, but it is inconveniently large for most liquids, so the millimetre-squared per second (mm²/s), equal to the centistokes, dominates practical tabulation. The Reynolds number, $Re = vL/\nu$, uses kinematic viscosity $\nu$ directly in m²/s.

Real-World Examples and Conversions

Water at 20 °C has a kinematic viscosity of about $1.004\times10^{-6}\ \text{m}^2/\text{s}$ (1.004 cSt). Air at 20 °C is roughly $1.5\times10^{-5}\ \text{m}^2/\text{s}$, higher than water because of air's low density. One $\text{m}^2/\text{s}$ equals $10{,}000\ \text{stokes}$ or $10⁶\ \text{mm}^2/\text{s}$.