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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Pressure Gradient
• Dimensions of Current Density
• Dimensions of Impedance
• Dimensions of Linear Density
• Dimensions of Rotational Kinetic Energy