Poise (unit)

The poise (symbol P; ) is the unit of dynamic viscosity (absolute viscosity) in the centimetre–gram–second system of units (CGS). 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 f o r c e × t i m e / a r e a {\displaystyle \mathrm {force\times time/area} } , that is, [ M 1 L − 1 T − 1 ] {\displaystyle [{\mathsf {M}}^{1}{\mathsf {L}}^{-1}{\mathsf {T}}^{-1}]} . 1 P = 0.1 m − 1 ⋅ kg ⋅ s − 1 = 1 cm − 1 ⋅ g ⋅ s − 1 = 1 dyn ⋅ s ⋅ cm − 2 . {\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): 1 Pa ⋅ s = 1 N ⋅ s ⋅ m − 2 = 1 m − 1 ⋅ kg ⋅ s − 1 = 10 P . {\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. 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). 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).