pound-force-seconds per square foot (lbf-s/ft2) to millipascal-seconds (mPa-s) conversion

What is the pound-force-second per square foot?

The pound-force-second per square foot (lbf·s/ft²) is the unit of dynamic (absolute) viscosity in the English/US customary gravitational system. It is sometimes called the "slug per foot-second" because it is numerically identical to that combination.

Definition

One pound-force-second per square foot is the viscosity that produces a shear stress of one pound-force per square foot at a shear rate of one per second:

$$1\ \text{lbf·s/ft}^2 = 47.8803\ \text{Pa·s}$$

The exact value follows from the definitions $1\ \text{lbf} = 4.4482216152605\ \text{N}$ and $1\ \text{ft} = 0.3048\ \text{m}$, giving $1\ \text{lbf·s/ft}^2 = 4.4482216152605 / 0.3048² = 47.880259\ \text{Pa·s}$ exactly. It equals one reyn's cousin in ft units, and is identical to $1\ \text{slug}\,\text{ft}^{-1}\,\text{s}^{-1}$.

Origin and History

The unit belongs to the foot-pound-second (FPS) gravitational system used by English-speaking engineers, in which force (the pound-force) rather than mass is a base concept. It became standard in aeronautical and mechanical engineering texts in the United States during the 20th century, where fluid properties were often tabulated in customary units.

Law and Notable Facts

It is not an SI unit; the SI equivalent is the pascal-second. A closely related unit, the reyn (1 lbf·s/in²), is used in lubrication engineering and equals $6.89476\times10^{3}\ \text{Pa·s}$, exactly 144 times the lbf·s/ft² because there are 144 square inches per square foot.

Real-World Examples and Conversions

Water at 20 °C, about $1.002\ \text{cP} = 0.001002\ \text{Pa·s}$, is roughly $2.09\times10^{-5}\ \text{lbf·s/ft}^2$. Conversely, $1\ \text{lbf·s/ft}^2 = 47.8803\ \text{Pa·s} = 47{,}880.3\ \text{cP}$, a very viscous fluid comparable to thick syrup. Air at room temperature ($\approx 1.8\times10^{-5}\ \text{Pa·s}$) is about $3.8\times10^{-7}\ \text{lbf·s/ft}^2$.

What is the Millipascal-Second?

The millipascal-second is a submultiple of the SI unit of dynamic viscosity, equal to one thousandth of a pascal-second. It is the everyday unit for the viscosity of liquids such as water, oils, and beverages.

Definition

One millipascal-second is one thousandth of a pascal-second, the SI derived unit of dynamic viscosity.

$$1\ \text{mPa-s} = 0.001\ \text{Pa·s}$$

In SI base units this is 10⁻³ kg·m⁻¹·s⁻¹. The millipascal-second is numerically identical to the centipoise (cP), the widely used CGS-based unit, so 1 mPa·s = 1 cP exactly.

Origin and History

The unit follows from the SI prefix "milli-" applied to the pascal-second, which itself was defined when the International System of Units systematized viscosity in terms of the pascal. Its convenience comes from matching the pre-existing centipoise, letting historical viscosity data carry over unchanged.

Law and Notable Facts

As an SI-sanctioned submultiple, the millipascal-second is fully standard. Its enduring popularity rests on a near-coincidence: liquid water at 20 °C has a dynamic viscosity of about 1.002 mPa·s, making the unit an intuitive reference point.

Real-World Examples and Conversions

• Water at 20 °C: about 1.0 mPa·s.
• Whole milk: roughly 2 to 3 mPa·s.
• Light motor oil (SAE 10 at operating temperature): tens of mPa·s.
• 1 mPa·s equals exactly 1 centipoise and 0.001 Pa·s.