Question

Find the conversion factor between the SI and CGS units of coefficient of viscosity using dimensional analysis.

Answer 1

The dimensions of the coefficient of viscosity η are

[η] = [ML^-1 T^-1]

The SI and CGS units of coefficient of viscosity are the pascal-second and poise, respectively.

1 Pa ∙ s = 1 N ∙ m^-2 ∙ s = 1 kg-m^-1 ∙ s^-1

1 P = 1 dyn ∙ cm^-2 ∙ s = l g-cm^-1 ∙ s^-1

Let 1 Pa ∙ s = xP

∴ 1[M₁ L₁ ^-1T₁ ^-1] = x[M₂L₂ ^-1T₂ ^-1]

where subscripts 1 and 2 pertain to SI and CGS units.