# Dimensions of Viscosity

## Dimensional Formula of Viscosity

The dimensional formula of Viscosity (η) is given by,

M1 L-1 T-1

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Viscosity = Tangential Force × Distance between layers × [Area × Velocity]-1 . . . . . (1)

Since, Tangential Force = M × a = M × [L T-2]

∴ The dimensional formula of Tangential Force = M1 L1 T-2 . . . . (2)

And, the dimensions of area and velocity = ML2 Tand MLT-1 . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Viscosity = Force × [Area × Velocity]-1 × Distance between layers

Or, η = [MLT-2] × [MLT0]-1 × [MLT-1]-1 × [MLT0] = [M1 L-1 T-1].

Therefore, viscosity is dimensionally represented as [M1 L-1 T-1].

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