pascal-seconds (Pa-s) to pound-force-seconds per square foot (lbf-s/ft2) 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-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 $3.8\times10^{-7}\ \text{lbf·s/ft}^2$.