pound-force-seconds per square foot (lbf-s/ft2) to poises (P) 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 Poise?

The poise is the unit of dynamic viscosity in the centimetre-gram-second (CGS) system, measuring a fluid's resistance to shear flow. It remains common in fields such as chemistry, food science, and petroleum engineering.

Definition

One poise is the viscosity of a fluid in which a shear stress of one dyne per square centimetre produces a velocity gradient of one reciprocal second.

$$1\ \text{P} = 0.1\ \text{Pa·s}$$

In SI terms, 1 poise = 0.1 Pa·s = 1 g·cm⁻¹·s⁻¹. The everyday subunit is the centipoise (cP), equal to 0.01 poise and to 1 millipascal-second, which is why water's viscosity is famously about 1 cP.

Origin and History

The poise is named after the French physician and physiologist Jean Léonard Marie Poiseuille (1797–1869), who studied the flow of liquids through narrow tubes, work later formalized as the Hagen–Poiseuille law. The unit was adopted within the CGS system in his honour.

Law and Notable Facts

The poise is not an SI unit, but it is accepted for continued use alongside SI in many industries. Its centipoise subunit is so entrenched that viscosity tables and specifications worldwide still quote values in cP even where the pascal-second is the formal standard.

Real-World Examples and Conversions

• Water at 20 °C: about 0.01 poise (1 centipoise).
• Air at room temperature: about 0.00018 poise.
• Glycerol at 20 °C: roughly 15 poise.
• 1 poise equals 0.1 Pa·s and 100 centipoise.