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 L1 T-1 . . . . (5)
On substituting equation (4) and (5) in equation (3) we get,
Dynamic viscosity (η) = [M L T-2] × [L] × [L2]-1 × [L1 T-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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