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 L¹ T^-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 × [L¹ T^-1]^-1 = [M¹ L^-1 T^-1].

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

⇒ Check Other Dimensional Formulas:

• Dimensions of Pressure
• Dimensions of Area
• Dimensions of Reynolds Number
• Dimensions of Rotational Kinetic Energy
• Dimensions of Impedance

Equation of Continuity

Surface Tension