# Dimensions of Coefficient of Viscosity

## Dimensional Formula of Coefficient of Viscosity

The dimensional formula of Coefficient of Viscosity is given by,

M1 L-1 T-1

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Coefficient of viscosity (η) = F × r × [A × v]-1 . . . . . (1)

Where F = tangential force, r = distance between layers, A = Area, and v = velocity

Since, Tangential Force (F) = Mass × Acceleration = M × [L T-2]

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

And, the dimensional formula of area and velocity = L2 and LT-1 respectively . . . . (3)

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

Coefficient of viscosity = F × r × [A × v]-1

Or, η = [M L T-2] × [L] × [L2]-1 × [LT-1]-1 = [M1 L-1 T-1].

Therefore, the Coefficient of Viscosity is dimensionally represented as [M1 L-1 T-1].