By Newton’s law of viscosity,

\(\frac FA\) = η\(\frac{dv}{dy}\)

where \(\frac FA\) is the viscous drag per unit area, \(\frac{dv}{dy}\) is the velocity gradient and y is the coefficient of viscosity of the fluid. Rewriting the above equation as

η = \(\frac{(F/A)}{(dv/dy)}\)

[η] = \(\frac{[FA^{-1} ]}{[dv/dy] }\)

= [ML^{-1} T^{-2} ][T^{-1}] = [ML^{-1} T^{-1}]

**SI unit:** the pascal ∙ second (abbreviated Pa ∙ s), 1 Pa ∙ s = 1 N ∙ m^{-2} ∙ s

**CGS unit:** dyne ∙ cm^{-2}∙ s, called the poise [symbol P, named after Jean Louis Marie Poiseuille (1799-1869), French physician].

[**Note : **The most commonly used submultiples are the millipascal-second (mPa ∙ s) and the centipoise (cP). 1 mPa ∙ s = 1 cP.]