# Find the dimensions of the coefficient of viscosity. State its SI and CGS units.

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Find the dimensions of the coefficient of viscosity. State its SI and CGS units.

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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.]