Question

Derive the dimension of viscosity

Answer 1

≡QUESTION≡

Derive the dimension of viscosity

                                                         

║⊕ANSWER⊕║

Coefficient of viscosity (η) = F × r × [A × v]-1 . . . . . (1)

Where

F = tangential force

r = distance between layers

A = Area

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 L¹T⁻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].

∴ The Coefficient of Viscosity is represented as [M¹ L⁻¹ T⁻¹].