pascal-seconds (Pa-s) to pounds per foot-second (lb/(ft-s)) conversion

What is the Pascal-Second?

The pascal-second is the SI derived unit of dynamic (shear) viscosity, measuring a fluid's resistance to flow. It quantifies the shear stress needed to produce a unit velocity gradient in a fluid.

Definition

One pascal-second is the viscosity of a fluid in which a shear stress of one pascal produces a velocity gradient of one reciprocal second between adjacent layers.

$$1\ \text{Pa-s} = 1\ \text{Pa·s}$$

Expressed in SI base units, 1 Pa·s = 1 kg·m⁻¹·s⁻¹ = 1 N·s/m². It is the coherent SI unit of dynamic viscosity and is exactly equal to 10 poise (the CGS unit), so 1 Pa·s = 1000 mPa·s = 1000 centipoise.

Origin and History

Viscosity was first characterized quantitatively through the work of Newton and later Poiseuille in the nineteenth century, with the CGS poise (named for Poiseuille) long serving as the standard unit. The pascal-second entered use with the adoption of the SI, tying viscosity directly to the pascal of pressure.

Law and Notable Facts

The pascal-second is the officially sanctioned SI unit of dynamic viscosity, though the millipascal-second (equal to the once-ubiquitous centipoise) remains far more common in practice because water at 20 °C has a viscosity of almost exactly 1 mPa·s.

Real-World Examples and Conversions

• Water at 20 °C: about 0.001 Pa·s (1 mPa·s).
• Air at room temperature: about 0.0000181 Pa·s.
• Olive oil at 20 °C: roughly 0.084 Pa·s.
• Honey: commonly 2 to 10 Pa·s depending on temperature and water content.

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 $0.134\ \text{lb/(ft·s)}$.