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.]
