square feet per second (ft2/s) to stokes (St) 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 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 $1\ \text{m}^2/\text{s} = 10{,}000\ \text{St}$.