Poise (unit)

The poise (symbol P; /pɔɪz, pwɑːz/) is the unit of dynamic viscosity (absolute viscosity) in the centimetre–gram–second system of units (CGS).^[1] It is named after Jean Léonard Marie Poiseuille (see Hagen–Poiseuille equation). The centipoise (1 cP = 0.01 P) is more commonly used than the poise itself.

Dynamic viscosity has dimensions of ${\displaystyle \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{\times }\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}/\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}}$, that is, ${\displaystyle [{\mathsf{M}}^1{\mathsf{L}}^{-1}{\mathsf{T}}^{-1}]}$.

$${\displaystyle 1\text{P}=0.1{\text{m}}^{-1}\cdot \text{kg}\cdot {\text{s}}^{-1}=1{\text{cm}}^{-1}\cdot \text{g}\cdot {\text{s}}^{-1}=1\text{dyn}\cdot \text{s}\cdot {\text{cm}}^{-2}.}$$

The analogous unit in the International System of Units is the pascal-second (Pa⋅s):^[2]

$${\displaystyle 1\text{Pa}\cdot \text{s}=1\text{N}\cdot \text{s}\cdot {\text{m}}^{-2}=1{\text{m}}^{-1}\cdot \text{kg}\cdot {\text{s}}^{-1}=10\text{P}.}$$

The poise is often used with the metric prefix centi- because the viscosity of water at 20 °C (standard conditions for temperature and pressure) is almost exactly 1 centipoise.^[3] A centipoise is one hundredth of a poise, or one millipascal-second (mPa⋅s) in SI units (1 cP = 10⁻³ Pa⋅s = 1 mPa⋅s).^[4]

The CGS symbol for the centipoise is cP. The abbreviations cps, cp, and cPs are sometimes seen.

Liquid water has a viscosity of 0.00890 P at 25 °C at a pressure of 1 atmosphere (0.00890 P = 0.890 cP = 0.890 mPa⋅s).^[5]

• Poiseuille
• Viscosity

et:Poise

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