pounds per foot-second (lb/(ft-s)) to millipascal-seconds (mPa-s) conversion

What is the pound per foot-second?

The pound per foot-second (lb/(ft·s)) is a unit of dynamic (absolute) viscosity in the English absolute (mass-based) system, where the pound is treated as a unit of mass (pound-mass). It is the FPS analogue of the poise, which is the gram per centimetre-second.

Definition

One pound per foot-second is the viscosity of mass one pound-mass flowing through one foot per second:

$$1\ \text{lb/(ft·s)} = 1.48816\ \text{Pa·s}$$

The exact value comes from $1\ \text{lb} = 0.45359237\ \text{kg}$ and $1\ \text{ft} = 0.3048\ \text{m}$, giving $1\ \text{lb/(ft·s)} = 0.45359237 / 0.3048 = 1.4881639\ \text{Pa·s}$. This is the pound-mass form and must not be confused with the gravitational pound-force-second per square foot, which is about 32.174 times larger.

Origin and History

This unit arises from the English absolute (or "poundal") system of mechanics, in which mass is the base quantity and force is the derived poundal. It appears in older engineering and chemical-engineering literature, particularly British texts, as a direct mass-based counterpart to the CGS poise.

Law and Notable Facts

It is not an SI unit. A useful relationship: $1\ \text{lb/(ft·s)} = 1{,}488.16\ \text{cP}$, and the difference between this mass-based unit and the force-based lbf·s/ft² is exactly the standard gravitational conversion factor $g_c = 32.17405$ (the ratio of pound-force to poundal).

Real-World Examples and Conversions

Water at 20 °C ($0.001002\ \text{Pa·s}$) is about $6.73\times10^{-4}\ \text{lb/(ft·s)}$. A fluid of $1\ \text{lb/(ft·s)} = 1.48816\ \text{Pa·s} = 1{,}488\ \text{cP}$ is roughly as viscous as light honey. Motor oil around $0.2\ \text{Pa·s}$ is about $0.134\ \text{lb/(ft·s)}$.

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.