Question

What is the dimensional formula for viscosity ?

Answer 1

Answer:

Mathematically, Coefficient of viscosity (η)= Fr/Av ——- F= tangential Force, Area, r= distance between the layers, v= velocity. Dimensional Formula of Force = M1L1T-2.

Answer 2

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].

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