square feet per second (ft2/s) to square millimetres per second (mm2/s) conversion

What is the square foot per second?

The square foot per second is an imperial and US customary unit of kinematic viscosity, expressing how quickly momentum diffuses through a fluid relative to its density. It appears in older engineering references and in fields where imperial units persist, such as parts of the oil and gas industry.

Definition

One square foot per second is the kinematic viscosity of a fluid in which an area of one square foot's worth of momentum diffusion occurs each second. Because one foot equals exactly 0.3048 metre, the conversion follows directly from squaring that length.

$$1\ \text{ft}^2/\text{s} = 0.0929030\ \text{m}^2/\text{s}$$

Exactly, $1\ \text{ft}^2/\text{s} = (0.3048)^2\ \text{m}^2/\text{s} = 0.09290304\ \text{m}^2/\text{s} = 92903.04\ \text{cSt}$.

Origin and History

The unit derives from the imperial foot, a length whose modern definition was internationally standardized in 1959 as exactly 0.3048 metre. Kinematic viscosity expressed in ft²/s follows the same dimensional pattern as its SI counterpart (m²/s), simply substituting the foot for the metre.

Law and Notable Facts

The square foot per second is a coherent unit within the foot–pound–second system rather than an SI unit. It is a comparatively large unit: even highly viscous industrial fluids rarely exceed a small fraction of 1 ft²/s, so most practical values are much less than one.

Real-World Examples and Conversions

• Water at 20 °C (~1.004 cSt) is only about $1.08 \times 10⁻⁵\ \text{ft}^2/\text{s}$.
• A heavy oil at 100 cSt equals about $1.076 \times 10⁻³\ \text{ft}^2/\text{s}$.
• $1\ \text{ft}^2/\text{s} = 0.09290304\ \text{m}^2/\text{s}$.
• $1\ \text{m}^2/\text{s} \approx 10.7639\ \text{ft}^2/\text{s}$.

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 $10⁻²\ \text{stokes}$.