poises (P) to centipoises (cP) conversion

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.

What is the centipoise?

The centipoise (cP) is a CGS unit of dynamic (absolute) viscosity, equal to one hundredth of a poise. It is the most widely used practical viscosity unit in industry because water at about 20 °C has a viscosity of very nearly 1 cP.

Definition

One centipoise equals one hundredth of a poise, which in SI units is exactly one millipascal-second:

$$1\ \text{cP} = 0.001\ \text{Pa·s}$$

Since $1\ \text{P} = 0.1\ \text{Pa·s}$ (the poise being defined as $1\ \text{g}\,\text{cm}^{-1}\,\text{s}^{-1}$), the centipoise is $10⁻²$ of that, i.e. $1\ \text{cP} = 1\ \text{mPa·s}$ exactly. The unit is dimensionally mass per length per time.

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 (blood) through narrow tubes and formulated what became the Hagen–Poiseuille law. The centipoise arose as a convenient submultiple because water conveniently sits near 1 cP, making comparisons intuitive.

Law and Notable Facts

The centipoise is a CGS-derived unit and is not part of the SI, which prefers the pascal-second (Pa·s) or millipascal-second (mPa·s). Because $1\ \text{cP} = 1\ \text{mPa·s}$ exactly, conversion between the everyday industrial unit and the SI unit requires no arithmetic beyond a change of name — a coincidence that has helped the centipoise survive.

Real-World Examples and Conversions

Water at 20 °C is about 1.002 cP. Whole milk is roughly 3 cP, olive oil around 60–80 cP, and honey near 2,000–10,000 cP. SAE 30 motor oil at 20 °C is on the order of 200 cP. To convert, $500\ \text{cP} = 0.5\ \text{Pa·s} = 500\ \text{mPa·s}$.