# Dimensions of Kinematic Viscosity

## Dimensional Formula of Kinematic Viscosity

The dimensional formula of Kinematic Viscosity is given by,

M0 L2 T-1

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Kinematic viscosity (ν) = Dynamic viscosity × [Density]-1.  . . . (1)

Since, Density = Mass × [Volume]-1

⇒ ρ = [M1 L0 T0] × [M0 L3 T0]-1

∴ The dimensional formula of density = [M1 L-3 T0] . . . . (2)

Since, Dynamic viscosity (η) = Tangential Force × distance between layers × [Area × velocity]-1 . . . . . (3)

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

∴ The dimensions of force = M1 L1 T-2 . . . . (4)

And, the dimensional formula of area and velocity = L2 and LT-1 . . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Dynamic viscosity (η) = [M L T-2] × [L] × [L2]-1 × [LT-1]-1 = [M1 L-1 T-1].

Therefore, the dimensions of dynamic viscosity = [M1 L-1 T-1] . . . .(6)

On substituting equation (2) and (6) in equation (1) we get,

Kinematic viscosity (ν) = Dynamic viscosity × [Density]-1

Or, ν = [M1 L-1 T-1] × [M1 L-3 T0]-1 = [M0 L2 T-1].

Therefore, the Kinematic viscosity is dimensionally represented as [M0 L2 T-1].

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