Dimensional Formula of Viscosity

The dimensional formula of Viscosity (η) is given by,

M¹ L^-1 T^-1

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Viscosity = Tangential Force × Distance between layers × [Area × Velocity]^-1 . . . . . (1)

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

∴ The dimensional formula of Tangential Force = M¹ L¹ T^-2 . . . . (2)

And, the dimensions of area and velocity = M⁰ L² T⁰ and M⁰ L¹ T^-1 . . . . (3)

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

Viscosity = Force × [Area × Velocity]^-1 × Distance between layers

Or, η = [M¹ L¹ T^-2] × [M⁰ L² T⁰]^-1 × [M⁰ L¹ T^-1]^-1 × [M⁰ L¹ T⁰] = [M¹ L^-1 T^-1].

Therefore, viscosity is dimensionally represented as [M¹ L^-1 T^-1].

⇒ Check Other Dimensional Formulas:

• Dimensions of Emf
• Dimensions of Wavelength
• Dimensions of Surface Tension
• Dimensions of Time Period
• Dimensions of Gravitational Potential Energy

Fulid Mechanics – Equation of Continuity

Fluid Mechanics- Surface Tension