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 ${\displaystyle \mathrm {force\times time/area} }$, 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]