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Identify the unit of dynamic viscosity from the following.
1. [MLT-2]
2. [ML-1T-1]
3. [ML-2T]
4. [M-1L-1T2]

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Correct Answer - Option 2 : [ML-1T-1]

Explanation:

From Newton’s law of viscosity

\(\tau = \mu \cdot \frac{{du}}{{dy}}\)

μ = Proportionality constant/ coefficient of viscosity or viscosity

μ = dynamic viscosity (since it involves force)

\(\therefore \mu = \frac{\tau }{{du/dy}}\)

Dimensional formula for μ

 μ = M.L-1.T-1

Units:

Dynamic Viscosity (μ):

SI system:

μ = N.s/m2 or Pa.s = kg/m.s

CGS system:

μ = Dyne.sec/cm2 = 1 poise

1 N = 105 dynes

1 N.s/m2 = 105 dynes.sec/104 cm2

1 N.s/m2 = 10 dyne.sec/cm2

1 N.s/m2 = 10 poise = 1 Pa.s

Now,

Kinematic Viscosity (v): It is the ratio of dynamic viscosity to mass density.

\(v = \frac{{Dynamic\;viscosity}}{{Mass\;density}} = \frac{\mu }{\rho }\)

Dimensional formula for Kinematic viscosity (ν)

 ν = L2T-1

The dimensions of the kinematic viscosity show that they involves the magnitudes of length and time only.

The name kinematic viscosity has been given to the ratio (μ/ρ) because its unit (m2/s) is similar to the unit of kinematic quantities like velocity (m/s) and acceleration (m/s2).

Units

SI system:

m2/sec

CGS system:

cm2/sec or stoke

1 stoke = 1 cm2/sec = 10-4 m2/sec

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